5. Suppose there exits positive differentiable a(x) and B(x) such that a*(x) – B°(x) = 3, and a'(x) = 53(x) (a) Assuming that a(x) exists (i.e., the inverse function of a(r) exists), compute an explicit formula for [a(x)]'. Hint: Follow the five step process we used to compute the derivative of In(x), arctan(x), etc.

Q: 1) Find the derivative of the given function with respects to e 3tan ở In 3 y

A: Given

Q: 2. Find the derivative of a function at a certain number using the formula. f(x) – f(xo) f'(x) = lim…

A:

Q: 1) Find the derivative of the given function with respects to e 3 tan 6 In 3 y

A:

Q: • Find f (x) of f(x)=by using the definition of the х-1 derivative. • 1- Find if y=3t-4 and t = Vx +…

A:

Q: 3. Find the derivative of the function. y = In(t2) – arctan(-

A:

Q: 9. Suppose for sume funchion f we have its derivative, f'x) = e*sin(x), on the %3D interval o< x<…

A: We can use application of derivative in order to solve the given problem.

Q: Calculate the derivative of the following function. 7 y = sin '(cos (3x)) If the Chain Rule only…

A: To find the derivative

Q: 1. Compute forward approximations of O(h) and O(h² for the first derivative of y = e* evaluated at x…

A: 1st we will derive formula for O(h) and O(h2) and then find corresponding values

Q: Compute the high-accuracy central difference approximation for the first derivative of y = cos x at…

A: There are three types of approximations to the derivative of a function f(x) at a point a. They are…

Q: Find the derivative of f (x) = Ln e*+1 using the limit process. %3D

A:

Q: In(5æ) Find the derivative with respect to x of y = %3D 5x y' = | %3D

A: Find the derivative

Q: 2. Find the derivative of y= ecos{/x+3) Solution:

A: Topic:- derivatives Note:- as per our guideline if more than one question uploaded than only first…

Q: Find the derivative of y with respect to the independent variable. x2 y =log 8 Sx+1 1 8x+1 O In8 x2…

A:

Q: 8. Find the derivative of the function. y= In(1+x)

A:

Q: Can you help me with this problem step by step?

A: The given equation,

Q: Find the derivative of y with respect to x. y = tan 1 (In 4x) 1+ (In 4x)2 xV1+ (In 4x)² x(1 + (In…

A: We will find the derivative of y with respect to x as following.

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. y= In(In 9x)

A: The solution for the above question is as shown below.

Q: 6. Differentiate: a. f(x) In (In (3x)) b. Find equation of the tangent line to the graph of y-e³x.…

A:

Q: In 5 x+1 Find the derivative of y = logs ((*)) with respect to x-1 independent variable x.

A:

Q: (3) Compute the derivative of the function e2t cos tdt.

A:

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 1-x (x+ 3)5 15) у - In 6х- 8 A)…

A: Given that:y=ln1-xx+35To find derivative

Q: # 5) Find the extrema points for the function f (x) = using the second derivative tes 1+x x2 %3D Fon…

A: To find the extreme points.

Q: Let y = x(ln x)² – 2x In x. Find the value of X for which the second derivative, y" (x), equals…

A: Solve the following

Q: 23.3 Use centered difference approximations to estimate the first and second derivatives of y = e*…

A: The formula for the first derivative of a function fx at x=a by centered difference approximation is…

Q: • Find f (x) of f(x)= by using the definition of the x-1 derivative. • 1- Find if y=3t-4 and t Vx+…

A: we have to find the derivative using definition. as per definition  f'(x)=limh→0f(x+h)-f(x)h

Q: b) Find derivative of the following: 1. y= 5x° + 2x -x + x* -9x+12 y=1-cos 20+3sine iI. ii. s= xln…

A: The detailed solution is as follows below:

Q: What is the first derivative of the expression (xy)^x = e? Hint: this involves implicit…

A:

Q: 9. Find the derivative of the function using chain rule. f(t) = 3t In t

A: To find the derivative of the function

Q: If y- sin x and yn) means "nth derivative of y with respect to x", what is the smallest posilive…

A:

Q: Y= In (In2 (1-x))re?

A:

Q: Calculate the derivative of the following function. y= sin (cos (3x)) If the Chain Rule only needs…

A: In the question we have to find derivative of the given function.

Q: 1) Find the derivative. Simplify where possible. y = x tanh-1x + In/1 – x²

A:

Q: 5- When the first derivative of the y = sinx function at x =pi/4 is calculated with the forward…

A: We will use basics of numerical methods here

Q: In (4x) Find the derivative of y with respect to x if y = sin (8 e') dt.

A:

Q: In x 3. Compute the approximate derivative of f(x) = · at x = 2, using three-midpoint x² + 1 formula…

A: Given is a function and at a point at which the approximate value of first derivative of the…

Q: 29. Prove the following derivatives by using the definition of derivative. (a) (") = n. dx nxn-1

A: topic - derivative and limits

Q: 3. F(x) = " In(x) (4t + et) dt. Find the derivative of F(x).

A: Given, F(x)=∫1ln(x)(4t+et)dt To find : Derivative of F(x) By using the second fundamental theorem of…

Q: (x² +SJ° In 14-X つ. dr

A:

Q: 1) Find the derivative of the given function with respects to 0 y = 3lan In 3

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

Q: 3. If the derivatives of h with respect to U; for h=²u

A:

Q: 2. Determine the 8th derivative of y with respect to x of the function 1 f(x) = 1+x2 and find the…

A: Taylor series

Q: 1.) Find the area under the curve y = x3 + 3x2 and the axis between x = 1 and x = 3.

A:

Q: (2) Assume that we have a Cobb-Douglas production function for a certain industry: Q = CL°K®, where…

A:

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = ln 3x + x

A:

Q: Suppose ln (x + 2y) = x4.Use implicit differentiation to find the derivative of y with respect to x.…

A: Differentiate the given function implicitly as follows.

Q: Suppose x6 e-5y = In (xy). Find Y by implicit differentiation. dx

A:

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = (cos θ) ln (2θ + 2)

A:

Q: Зх +1 a) y =- 1 b) g(x)= Jx -

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Q: 11 with respect to x is The derivative of y = cos - 1

A: