Okay, so we see that we have a product of two transparent So when we take the derivative, let's use our product rule Just, um, two hands One a half So that's this extra part of negative 1/2 times for X 12 part of negative one and then plus distributive off this term here, that's negative or X plus one That's part of negative one of minus wanted it to go to an end Times conservative of1 For Windows or Linux Press CtrlD 2 For MacOS Press CmdD 3 For iPhone (Safari) Touch and hold, then tap Add Bookmark 4 For Google Chrome Press 3 dots on top right, then press the star signLet y = 1 x2 1 x2 is the same as x−2 ⇒ dy dx = − 2 ⋅ x−2−1 = − 2x−3 ⇒ dy dx = − 2 x−3 Answer link KillerBunny To find the derivative of a ratio, apply the formula
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Horizontal derivative of x 2 - xy + y 2 1-Implicit differentiation can help us solve inverse functions The general pattern is Start with the inverse equation in explicit form Example y = sin −1 (x) Rewrite it in noninverse mode Example x = sin (y) Differentiate this function with respect to x on both sides Solve for dy/dxDifferentiate (x^2 y)/(y^2 x) wrt x;
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Two straightforward ways Method One Rewrite as (1 x2)−1 and use the power and chain rules h'(x) = −(1 x2)−2 ⋅ 2x = − 2x (1 x2)2 Method Two Use the quotient rule d dx ( f (x) g(x)) = f '(x)g(x) − f (x)g'(x) (g(x))2 h'(x) = 0 −2x (1 x2)2 = − 2x (1 x2)2 Answer linkThe procedure to use the second derivative calculator is as follows Step 1 Enter the function in the respective input field Step 2 Now click the button "Submit" to get the derivative Step 3 Finally, the second order derivative of a function will be displayed in the output fieldMore free lessons at http//wwwkhanacademyorg/video?v=Mci8Cuik_Gw
Derivative of 1/ (xy) (1/ (xy))' ( (1)'* (xy) (1* (xy)'))/ ( (xy)^2) (0* (xy) (1* (xy)'))/ ( (xy)^2) (0* (xy) (1* ( (x)' (y)')))/ ( (xy)^2) (0* (xy) (1* ( (y)'1)))/ ( (xy)^2) (0* (xy) (1* (01)))/ ( (xy)^2) (0* (xy) (1*1))/ ( (xy)^2) 1/ ( (xy)^2)Example 1 Find each of the directional derivatives D→u f (2,0) D u → f ( 2, 0) where f (x,y) = xexy y f ( x, y) = x e x y y and →u u → is the unit vector in the direction of θ = 2π 3 θ = 2 π 3 D→u f (x,y,z) D u → f ( x, y, z) where f (x,y,z) = x2zy3z2 −xyz f ( x, y, z) = x 2 z y 3 z 2 − x y z in the direction of →vApply the quotient rule, which is and To find Apply the product rule;
Differentiate using the Power Rule which states that d d x x n d d x x n is n x n − 1 n x n 1 where n = 1 n = 1 Since − 1 1 is constant with respect to x x, the derivative of − 1 1 with respect to x x is 0 0 Simplify the expression Tap for more steps Add 1 1 and 0 0 Multiply − 1 1 by 1 1The Derivative tells us the slope of a function at any point There are rules we can follow to find many derivatives For example The slope of a constant value (like 3) is always 0;The easiest way is to expand the square as x 2 \frac1x You should be able to differentiate this Alternatively it is a composite function First differentiate the square 2\left(\sqrt{x}\frac1{\sqrt{x}}\right), then multiply by the
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Find the Derivative f(y)=y/(x^2y^2) Differentiate using the Quotient Rule which states that is where and Differentiate Tap for more steps Differentiate using the Power Rule which states that is where Multiply by By the Sum Rule, the derivative of with respect to isDerivative of 1/ (x^2) \square!Derivative of x/(x^2y^2) by x = (y^2x^2)/(y^42*x^2*y^2x^4) Show a step by step solution;
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Answer to Find the derivative dy/dx if y(x) = sqrt(x^2 1) By signing up, you'll get thousands of stepbystep solutions to your homeworkSo with y=(x)/(x^21) Then { (Let u=x, =>Professionals For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music
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Tan x) Next, y'(x)= 2 sec2x tan x Derivative of sec x degree We have the derivative of sec x degree So, y is equal to sec x degree However, we know the pi valueDerivative x^2(xy)^2 = x^2y^2 Natural Language;Find the Derivative f(x)=x^22x1 Differentiate Tap for more steps By the Sum Rule, the derivative of with respect to is Differentiate using the Power Rule which states that is where Evaluate Tap for more steps Since is constant with respect to
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Dy/dx = x(1 2x^2)/y =>Free secondorder derivative calculator second order differentiation solver stepbystep This website uses cookies to ensure you get the best experienceDerivative of x^2 y x y^2 in the direction (1,1) WolframAlpha Area of a circle?
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If y = xsqrt(1 x^2) then y^2 = x^2(1 x^2) = x^2 x^4 Now differentiate implicitly 2ydy = (2x 4x^3)dx, therefore, cancel 2s and x and make dy/dx the subject of the formula ydy = (x 2x^3)dx = x(1 2x^2)dx =>About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy &Y = xe^(x^2), Find the derivative of the function
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Answer (1 of 4) y= log {x(x^21)^1/2} Let x=tanA , dx/dA = sec^2A(1) y = log { tanA(tan^2A1)^1/2} y= log (tanAsecA) dy/dA= 1/(tanAsecA) (sec^2AEasy as pi (e) Unlock StepbyStep Natural Language Math Input NEW Use textbook math notation toKnowledgebase, relied on by millions of students &
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Solution We find that the derivative of x 2 is equal to 2x Checking Your Work In order to check our work, we can take the indefinite integral, akaGet stepbystep solutions from expert tutors as fast as 1530 minutes Your first 5 questions are on us!Derivative calculator This calculator evaluates derivatives using analytical differentiation It will also find local minimum and maximum, of the given function The calculator will try to simplify result as much as possible
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When x = 5, then y = x3 = 125, so that the pair (5, 125) solve that equation 125 = 75 At last, the derivative of sec square x is 2 sec squared x times tan x Let, y = sec x By power rule and chain rule, y'(x) = 2 secx d/dx (sec x) Next, y'(x)= 2 sec x 60 seconds Report an issue Q Find the derivative of the given equation f (x) = x 4 4x 3 2x 2 answer choices x 3 x 2 x 4x 3 12x 2 4x 4x 12x 4x 4x 3 12x 2 4x
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Derivative of (8x^2^y4x^y7) (3x^2^y7x^y16) Simple step by step solution, to learn Simple, and easy to understand, so don`t hesitate to use it as a solution of your homework Below you can find the full step by step solution for you problem We hope it will be very helpful for you and it will help you to understand the solving processThanks y = cos(x) 3 the inverse of this is x = cos(y) 3 solve for y and you have your inverse The cos function only has a range of 1,1, so the range of f(x) is 2,4 this means Calculus Let f be a twicedifferentiable function defined on the interval 12 less than or equal to x less than or equal to 32 with f(1)=2Free PreAlgebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators stepbystep
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How to differentiate the natural exponential function using chain rule d/dx of e^(x^2)If g (x) is a polynomial of degree ≤ 3 such that ∫ f (x) g (x) d x does not contain any logarithm function and g (− 2) = 1 0 Then Then The equation f ( x ) = 0 hasGet stepbystep solutions from expert tutors as fast as 1530 minutes Your first 5 questions are on us!
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Derivative z (x)= (x2)^21 \square!Derivative of arctanx at x=0;Answer (1 of 6) I assume you want to differentiate with respect to x Then (\frac{d}{dx})(\frac{x}{2}) Constant can be taken out of the differentiation Which gives \frac{1}{2}\times(\frac{dx}{dx}) Which gives \frac{1}{2}(1) Hence the answer is \frac{1}{2} Hope this helps
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Extended Keyboard Examples Upload Random Compute answers using Wolfram's breakthrough technology &In doing this, the Derivative Calculator has to respect the order of operations A specialty in mathematical expressions is that the multiplication sign can be left out sometimes, for example we write 5x instead of 5*x The Derivative Calculator has to detect these cases and insert the multiplication sign5 b Therefore, b = −250 The equation of the tangent is y = 75 x − 250 Problem 3 Prove The straight line that is tangent to y = x2 at the point ( a, a2 ), bisects the distance of a from the origin
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Enter your queries using plain English To avoid ambiguous queries, make sure to use parentheses where necessary Here are some examples illustrating how to ask for a derivative derivative of arcsin;An online derivative calculator that differentiates a given function with respect to a given variable by using analytical differentiation A useful mathematical differentiation calculator to simplify the functions 1 Write (10x2)(x 2) as 10*x2x^2 2 Write cos(x 3) as cos(x^3) 3 WriteAnswer (1 of 6) What is the derivative of (√x 1/√x) ^2?
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Answer (1 of 7) y=x^{1/2} \dfrac{dy}{dx}=\dfrac{1}{2}x^{1/2} \dfrac{dy}{dx}=\dfrac{1}{2x^{1/2}} \dfrac{dy}{dx}=\dfrac{1}{2\sqrt{x}} mathy=x^{1/2}/math math\dfrac{dy}{dx}=\dfrac{1}{2}x^{1/2}/math math\dfrac{dy}{dx}=\dfrac{1}{2x^{1/2}}/math math\dfrac{dy}{dx}=\dfrac{1}{2\sqrt{x}}/mathAt a point a ∈ R 2, the directional derivative of a di ff erentiable function f (x, y) in the directions (1, 1) and (1, − 1) equals 3 and 2 respectively Find the largest rate of change of f ( x, y ) at a , and the direction in which it occursThe Derivative Calculator supports solving first, second, fourth derivatives, as well as implicit differentiation and finding the zeros/roots You can also get a better visual and understanding of the function by using our graphing tool Chain Rule d d x f (g (x)) = f ' (g (x)) g ' (x) Step 2 Click the blue arrow to submit
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Second derivative of sin^2;Derivatives Derivative Applications Limits Integrals Integral Applications Integral Approximation Series ODE Multivariable Calculus Laplace Transform Taylor/Maclaurin Series Fourier Series Functions Line Equations Functions Arithmetic &Transcribed image text Question 1 (3 marks) 1 Find the first derivative y = x x2 Question 2 (3 marks) 31n (x) Find the first derivative of y = x2 Hint Use the quotient rule Question 3 (3 marks) Find the first derivative of y = €5x2 7x13 =e Question 4 (4 marks) = 1 = You are given the utility function U = 10x04 yo6, for goods X and Y, prices Px = 2 and Py = 4 and a budget constraint
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, (du)/dx=1), (And v=x^21, =>, (dv)/dx=2x ) } d/dx(u/v) = (v(du)/dxu(dv)/dx)/v^2 dy/dx = ( (x^21)(1) (x)(2x) ) / (x^21)^2 dy/dx = ( x^21 2x^2 ) / (x^21)^2 dy/dx = ( 1x^2 ) / (x^21)^2The slope of a line like 2x is 2, or 3x is 3 etc;To find Differentiate term by term The derivative of the constant is zero Apply the power rule goes to The result is
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And so on Here are useful rules to help you work out the derivatives of many functions (with examples below)Note the little mark ' means derivative of, andSafety How works Test new features Press Copyright Contact us CreatorsCalculus Find the Derivative d/dx y=3x^2 y = 3x2 y = 3 x 2 Since 3 3 is constant with respect to x x, the derivative of 3x2 3 x 2 with respect to x x is 3 d dx x2 3 d d x x 2 3 d dx x2 3 d d x x 2 Differentiate using the Power Rule which states that d dx xn d d x x n is nxn−1 n x n 1 where n = 2 n = 2 3(2x) 3 ( 2 x)
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Chemical Engineering Chemical Engineering questions and answers 11 Determine the first derivative of y = (sin1x)2 arcsinx sin1x 1 y' V1x2 2sin 1x1 2 y' = 7172 3 y' = 2x1 122 2sin1x1 4 y' = Vx21 tan1x 12 Determine the first derivative of y = 1 y' = x (1x2)tan1x 2 y' = x (1x2)tanlx x2 (1x2) 3 y' = xtan18 x²Draw graph Edit expression Direct link to this page Value at x= Derivative Calculator computes derivatives of a function with respect to given variable using analytical differentiation and displays a stepbystep solution It allows to draw graphs of
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