2. Find the derivative of g(x) = 2x sin x.

Q: Find the 5th derivative of the function y=x2sin2x at x=0.

A:

Q: find the derivative of the function  f(x) = e5x sec x

A:

Q: 4. Find the derivative of the function f(x) = (sin x)c0s ". COS x

A:

Q: Find the 2nd derivative of y with respect to x : y=xe^2x

A:

Q: Find the derivative of the function.…

A: The given function is hx=x2arctan8x

Q: B. By using the definition of the derivative, find the for: - dx f(x) = x -

A: Explanation of the answer is as follows

Q: Find the derivative of the function

A:

Q: Find the derivative of y with respect to x of y = xlnx – x.

A: Using rules of differentiation.

Q: X+3

A:

Q: Determine the derivative of f(x)=ln(x√x^2+1).

A:

Q: Find the derivative of the function.

A: Given y=lnx+1x-1

Q: Find the derivative of the function. y = ln√(x2 − 4)

A:

Q: 10. Determine the derivative of the function with respect to x. y = sin?(x)

A:

Q: 4. Consider the function f(x) = 2 cos x x2 find its derivative

A: (4) Consider the given function. fx=2cosxx2 The quotient rule is defined as. fxgx'=f'g-g'fg2

Q: Find the second derivative of the function. y = x sin2 x

A: Given information: The function is y==xsin2x To find the second derivative, first differentiable…

Q: Find the indicated derivative of the function. for y = -4 cos X dx4

A:

Q: Find the derivative of y=. =x²- 1 2 COS X

A: Given,  y=x2-12cos x

Q: Find the derivative of the function. y = 2 cos5 x

A: Given, y = 2 cos5 x To evaluate, dydx

Q: Find the derivative of the function. f(x) = 6√x + 5 cos x

A: To find the derivative of the given function f(x).

Q: Find the derivative of the function y = ln(9 – e-"). f'(x) =

A: Given that y=ln(9-e-x) To find : Differentiation  y'=f'(x)=ddx(ln(9-e-x))=19-e-xddx(9-e-x)=e-x9-e-x

Q: Find the derivative of y = sin(-* e-X 2ex + 1

A:

Q: Find the derivative of the function. y = x/2 − sin 2x/4

A: Given function is y=x2-sin2x4 We have to find derivative of given function. Differentiating the…

Q: Find the derivative of the function .

A: Given a function f(x)=2x3+3 cos x f(x)=2(x)1/3+3 cos x      =2x-1/3+3 cos x We, use the following…

Q: 1 14) Use the definition of derivative to find dx 3- х.

A:

Q: Find the derivative of the function. 10 f(x) = 3 + 2cos x

A: Recall: dxndx=n xn-1 d(cos ax)dx= a(- sin ax) dc1f(x)±c2 g(x) dx= c1d[f(x)]dx± c2d[g(x)]dx

Q: Find the derivative of the function y = e2x tan 2x

A:

Q: Find the derivative of the function:  y= x sin 3/x

A:

Q: 1. Find the derivative of the function sin (4x) f (x) = V 3x

A:

Q: 2. Find the derivative of the function. y = e* In (sinæ)

A:

Q: Find the second derivative of the function f(x) = sin x2

A: Given f(x) = sin x2 To find d2f(x)dx2

Q: 2. Find the derivative. a. y = sin x

A:

Q: y = cof'/ x2-1 x²+

A:

Q: Find the derivative of the function. 10 f(x) = + 6cos x Vx

A: Differentiate above equation with respect to x

Q: Find the derivative of the function y = x2 Sin x - 2 Cos x.

A: y=x2sinx-2cosx

Q: Find the derivative of y = x 1 cOS x 2

A:

Q: Find the derivative of the function. y = ln(x√x2 − 1 )

A:

Q: Determine the 8th derivative of y with respect to x of the function : f(x) = 1 / 1 + x2 and find the…

A:

Q: Find the derivative of g(x) = e-" cos(x²)

A:

Q: Find the derivative of y with respect to x    y=ln(x-7)

A:

Q: Find the first derivative of y = cos*x- sin*x.

A:

Q: 1. Find the first order derivative of u = x*.

A:

Q: 2x Find the second order derivative of y = Tan 1-x

A:

Q: c. Find the derivative of y =+- et x3 cOS X 2

A:

Q: Find the derivative of the function. y [x + (x + sin²(x))-1*

A:

Q: Find the derivative of V(x) = ln(sin x) – (x4 – 3x)10

A: We can find the derivative as below.

Q: Find the derivative of the function f(x) = sinh 9x

A:

Q: Find the derivative of f(x)= ln x^2/x^2+1

A:

Q: Find the derivative of the function. y = x sin 1/x

A: Given: y=xsin1x We know that ddxu.v=vdudx+udvdx                                                  ..1