Find the general anti-derivative of f(x) = + Vx on a continuous interval.

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

A:

Q: Find the derivative of the function.…

A: The given function is hx=x2arctan8x

Q: Find the derivative of the function.

A: Given function is By using the properties of logarithm, ln(a/b)=ln(a)-ln(b) and ln(a^b)=bln(a), we…

Q: Compute the derivative of F(x) if F(x) = 9t dt F'(x) =

A: To find the derivative of integral, one have to use the fundamental law of calculus and substitute…

Q: Find the derivative of f(x) = 3x° cos(x). 8 CoS f'(x)

A: Given query is to find the derivative of the function.

Q: Define the derivative of f(x) at x

A: Consider a function f(x) The differentiability of a function:  Let f(x) be a real valued function…

Q: What is the derivative of the function f(x)=1/x+1 at x=1?

A: To find out the derivative of the function at x=1

Q: find the derivative of f (x) at the designated value of x. f (x) = 1x at x = 1/16

A: Given: fx=1x To find the derivative  Differentiate the given function with respect to x we get,…

Q: Apply the second derivative test to find all relative extrema. (c) f(x) = 1

A: To find the relative extrema first we  find the critical points. The critical points are the values…

Q: State the theorem for Second Derivative Test for f (x, y).

A: The second-derivative test for maxima, minima, and saddle points has two steps. 1. Find the critical…

Q: Find the derivative of the function y = arctan x + x 1+x²

A: Given: y=arctanx+x1+x2Recall the formulas:ddxarctanx=11+x2     ..........1ddxuv=vdudx-udvdxv2…

Q: X+3

A:

Q: Find the derivative of the function. F(x) = et dt

A: The function is given as F(x)=∫xx2et4 dt. The Leibnitz rule of differentiation under the integral…

Q: What is the derivative of f(x) = - 3 with respect to r? %3D

A: Given: The function f(x)=-3x3

Q: Determine the derivative of f(x) = ( In x )6 with respect to x. f'(x) =

A:

Q: Find the derivative of the function. f(x) = 2x In(x) f'(x) =

A: Let us consider the given function as: fx=2xlnx By using product Rule of derivative, we get:…

Q: Find the derivative of the function. 1 3x' g(x) = dt 1 + t4 Jtan x

A: Given : g(x) = ∫tanx3x211+t4dt

Q: What is the derivative of the function with respect to x of (x + 1)³ – æ° -

A: Given : Function x+13 - x3   To find : Derivative of the given function with respect to x?

Q: Find the derivative of the function. rlx) = [in[x*}}°

A:

Q: Find the derivative of the function. x + 6 X-6 y' = y = In

A: I have appended the formula used in the solution part of the question.

Q: Calculate the 4th derivative of the function y=x2/x−1 at x=2.

A:

Q: Find the derivative of the function. 3x2 g(x) • dt 4 + t3 tan x g'(x) =

A:

Q: p(x) = In(x)^/x

A:

Q: find the derivative of f (x) at the designated value of x. f (x) = x + 11 at x = 0

A: To find the derivative of f(x)=x+11 at x=0 Solution: f(x)=x+11 Differentiating both sides w.r.t x we…

Q: Compute the derivative of the fo f(x)= 2x+3x ex

A:

Q: f(x) = x In x

A:

Q: Find the derivative of the function. h(x) = x² arctan(8x) %3D

A: To find the derivative of hx=x2tan-18x

Q: 3x g(x)=e* In(4x+1) (с)

A:

Q: Find the derivative of the function. • 2x2 g(x) = 1 dt 3 + t3 /tan x g'(x) =

A:

Q: Find the derivative of the function y= arctan x +x/1+x2

A:

Q: Find the derivative (x) = 2 In x – Vĩ

A: Given: fx=2lnx-x   As we know that; The sum/difference rule:  f±g'=f'±g' The Power law; ddxxn=nxn-1…

Q: find the derivative of f (x) at the designated value of x. f (x) = x5 at x = 3/2

A: Given function is: fx=x5 We have to find the derivative of f(x) at x=32. Then we get,…

Q: Compute the derivative of f (x) = (x – 3r) cos(r). -

A: You will find the derivative of the given function using the product rule of differentiation which…

Q: Find the first derivative of the function of f(x) using any method?

A: Given,

Q: Find the derivative of f(x) = v3x + 1 using the general formula for differentiation.

A:

Q: find the derivative of y with respect to the appropriatevariable. y = csc-1 (x2 + 1), x > 0

A: Given that, y=csc-1x2+1

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. f(x) = 18 In(x) %3D

A: Derivative Question

Q: 4. F(x) = (1-t) dt

A: To find the first derivative

Q: Find the derivative of the function.   y = In(x)/x9

A:

Q: Use a quick approximation to estimate the derivative of the given function at the indicated point.…

A: f (x) = 1 − 2x  point,  x = 2 To use quick approximation to estimate the derivative, f'(2).

Q: What is the first-order derivative of y = x^y?

A:

Q: f(x) = x*Inx

A: TO FIND 5th order derivative f(x) = x4 lnx FORMULA USED  BIPART PRODUCT RULE OF DIFFERENTIATION…

Q: Find the derivative of f(x) = 4e 3x + e -x^2 f(x)= ?

A:

Q: Find the derivative of the function. x + 4 f(x) = In X – 4 | f'(x) =

A:

Q: What is the derivative of the function B(x)=3/(x+2) at x=a?

A:

Q: Calculate the derivative of the function y=x2−x−1x without using the quotient rule.

A:

Q: Find the derivative of the function. 1 g(x) = dt Jtan(x) V2 +

A:

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

A: