A three times differentiable function fwith f'(x) 0 has a D-derivative at x given 2 f'"(x) 3(f"(x) Df(x)=(x) 2 f(x), 1. Compute Df(x) where f(x) = ex. 2 2. Show that D(f o g)(x) ((Df) g)(x) (g'(x))Dg(x) - Assuming that both Df(x) and Df-1(x) exist, find a formula for Df-1(x) 3. X tnt dt for t > 0. 4. Compute Df-1 (0) where f(x) = 1

Q: Find the relative extrema using both First and Second Partial Derivative test f(x) = Sin2x ; 0<x<n

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A: The resulting change in function f (x, y) is given as:

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Q: Find the derivative. 2 - - dy dx - if y(x) = 1 x + 3 dy dx ||

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A: We have to find all second order partial derivative with respect to variable x and y: Given:

Q: 3. The derivative of /(x) = In x at x = 3 when hourrent = 0.001 and hprevious = 0.002

A: Given problem:- 3. The derivative of f(x) = In x at x = 3 when hcureent= 0.001 and hprevious = 0.002…

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A: y=uxvx, where ux  &amp;  vx are the differential functions of x. To differentiate these type of…

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A:

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A: The derivative of y=sech-1(lnx)+esinh-1(3x) is to be calculated by chain rule. The derivative of…

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A:

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A: We have to find

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Q: To investigate these values, we find the second derivative f"(x) = %3D At the positive critical…

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A: We have to find total derivative of u with respect to 'x'    where     u = 6 x2 + 4 y2 + 4 z2  Given…

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A:

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A: To find the extreme points.

Q: If f(x) is odd function, then the derivative of y=sinh (f (-x)) equals Select one: o y'=Xf'x) – f x)…

A: Differentiate wrt x

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A: According to the Leibinitz rule :

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Q: 1 point) Find dy/dx by implicit differentiation. 2cos(x)sin(2y)=−4 dy/dx=dy/dx

A: It is implicit differentiation.

Q: 1 log3(r – y)*

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A: Given

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A:

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A: Topic = Derivative

Q: Explain of the method of proving the derivative (dy/dx) of y= U(x)V(x) where U(x)and V(x) are…

A: We have to explain of the method of proving the derivative dydx of y= U(x)V(x) where U(x)and V(x)…

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A: We will find an example

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A: Solution is given below:

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A:

Q: Explain of the method of proving the derivative (dy/dx) of y= U(x)"(») where U(x)and V(x) are…

A: The function is, y=U(x)V(x)

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Q: A curve y = /(x) have length of the curve from x 0 to x= n/2. dy Vcos(2x - 2) as its first…

A: