For the above function f( x ) = 2 · 1.3ª, estimate ƒ'(x) using h= 0.001 for the following three values. f'( – 3.75) = Preview f'( – 0.75) = Preview f'(2) = Preview

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

A: f(x) = ln(sinh(x)) here we use chain rule f'(x) = cosh(x)/sinh(x) f'(x) = cot(h(x))

Q: Find the 4th-order derivative of the function y=xsinhx.

A:

Q: Find the second derivative for the functions defined as follows.h(x) = x/ex

A: Given:             f(x)=xex

Q: Find the second order derivative of f(x) exsinxcos2x

A:

Q: Find the derivative of the following functions using the long method (limits) (a) x =t-5t- 3 (b) y =…

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Q: Find the nth-order derivative of the function y=arctanx at the point x=0.

A:

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: What is the average rate of change of the function f(x): = x² between x = -3 and x = 3?

A:

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: Use backward, forward, and centered difference approximation to estimate the second derivative of…

A: We will do all three parts.

Q: Find the derivative of the function. f(x) = In(x + 1) f'(x) =

A: To find the derivative of the function fx=lnx+1

Q: L(x) = In(x)+log,(x)

A: Used formulas : ddx(logax) = 1x ln a ln x = loge xloge e = ln e = 1ln 5 =1.61

Q: Use the first derivative test to find the location of all local extrema in the interval for the…

A:

Q: Evaluate the derivative at x = 1 for y = In ()

A: For a function f its derivative is defined as f'(x)=limh→0f(x+h)-f(x)h. For some standard functions…

Q: Find the derivative of the function below. F(x) = arctan e a*) f'(x) =

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: Defermine the derivative of the following functions using the long method (using limits). 1. y =t –…

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Q: The nth derivative of y = Inx is given by %3D

A:

Q: Find the derivative of the function g(x)= tanx/e^x.

A: This problem can be solved by the quotient rule in derivatives.

Q: Find the derivative of f(x)=arctan(1/x) and simplify

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Q: Find the derivative of the function f(x) = coth−1(x2)

A:

Q: 2) Find nth derivative of the following function f(x) = ex

A: Given query is to find the nth derivative of the expression.

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: or x>0, determine the deriva

A: Consider the given function: Here the objective is to find the derivative of a given function using…

Q: Evaluate the derivative at x = 1 for y = I (

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Use forward and backward difference formula with h = 0.1 to approximate the derivative of f(x) =…

A:

Q: Find the derivative of the function y = (1/2) arctan e2x

A: Given function is y=12tan-1e2x Chain rule of differentiation states that: ddxfgx=f'gxg'x And also we…

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

A:

Q: Match the graph of the above function with the graph of its derivative. 0 ㅇ O 수 +

A: The given graph of the function is the graph of a semi circle. Or positive side of the circle.

Q: Find the derivative of the function. f(z) = V - VE f '(x) =

A:

Q: f(x) = x In x

A:

Q: Find the derivative of the function g(x)= integral  x2  tanx  (1/square root 4+t4) dt

A: Leibnitz integral rule for Differentiation :               ddx ∫α(x)β(x) f(t,x) dt = ∫α(x)β(x)…

Q: Find the (a) approximate error and (b) relative approximate error of the following: The derivative…

A:

Q: What is the Derivative of the following function;  y = Arctan 2(x 3)

A: To find: The derivative of y=tan-1x32. Formula used: Chain rule of derivative: fgx'=f'gx·gx Power…

Q: Find the derivatives from the left and from the right at x = 1 (if they exist). Is the function…

A:

Q: Find the derivative of the following functions using the long method (limits) y= tan x

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Use the Chain Rule combined with other differentiation rules to find the derivative of the following…

A: Given: y=xx+15 To Find: The derivative of the given function

Q: Find the derivatives from the left and from the right at x = 1 (if they exist). Is the function…

A: Given: f(x)=(1-x2) Find the derivative of given function from the left and from the right at x = 1…

Q: The derivative of xª at x = e is equal to .Soloot ono

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Q: find the derivative of y with respect to the givenindependent variable. y = log2 5θ

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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 the function.

A:

Q: 2. Use the second derivative to find the inflection points and the intervals on which f(x) is…

A: For inflection point, Put f"(x)=0. For concave upward, f"(x) > 0. For concave downward, f"(x)…

Q: The derivative of y=eSinh/x +cosh¬/x equals

A:

Q: Find the nth order derivative of the function y=xlnx.

A:

Q: What is the first derivative of s(x)=(7x)3x at x=4? Select the correct answer below:…

A: As s(x)=(7x)3x The function can be rewritten as:s(x)=x3x. 73xIts first derivative is given by the…

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

A:

Q: Find the first derivative or f(x) of the following functions using the techniques of integration.

A:

Q: Find the derivative. f(x)=tanh(2 + e^3x)

A:

Q: Find the approximate value of derivative f'(0) with the step size h for the following function by…

A: