a) Suppose F(x) is a differentiable function for all real numbers x. Evaluate the following derivative. Enter the derivative of F(x) using prime notation, i.e., as F'(x). d/dx (F(x4)) = _____

Q: 2. Determine the derivatives of the functions given below using only algebra and the specified…

A: Part a,Given,           fx=-x23+x3x104

Q: Let y = (2x + 3 sin(x))4. Find f(x) and g(x) so that y = f(g(x)) and compute the derivative using…

A:

Q: 4. Consider the function g(x) = r+3° a) Find the derivative of g using differentiation rules. b)…

A: The given function, g(x)=2x+3

Q: 1. Determine the true error and relative true error when approximating the derivative of ƒ(x) = -x²…

A: solution is here

Q: 5. Calculate the derivative of the following functions. DO NOT SIMPLIFY a. f(x) = x³ (arctan(x²) –…

A:

Q: 1.) Using the DEFINITION (using Ax or h) of derivatives, compute for the derivative of the function…

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

Q: 1 Find the derivative of f(x) = - at x= 3 %3D (Type an integer or a simplified fractic 21 %3D

A:

Q: 5a) Using the formula man = lim+)=/G2 determine the derivative/ slope of tangent for h→0 the given…

A:

Q: a. Find the derivative of f(x) = x2 - 5x at x. That is, find f′(x). b. Find the slope of the tangent…

A: Given: fx=x2-5x To Find: a. f'x=?b. Slope of tangent line of the given function at x=-1 and x=3

Q: Consider the function f(x) = V1 – 5x. a. Use the \underline{limit definition of derivative} to find…

A: We have to find the following given condition

Q: 10 Find the derivative f'(0) of f(x) = at x + 4 x = 0 using the laws of differentiation.

A: Derivative of the function

Q: a. What is the analogous formula for the derivative of the product uvw of three differentiable…

A: Concept:The derivative formula of two product functions is as follow:

Q: 5. (a) Use the limit definition of the derivative to find the derivative of f(r) = /5I+1. %3D

A:

Q: 1. Find a, b, and c such that the function f(x) has a derivative at x=0 and x=2, where: tan-1(x);x…

A:

Q: (a) Let f be a function that is continuous everywhere and let F(x) = {(f(x) sin^2(x))/x  , if x ≠0…

A: We need to apply formula of derivative

Q: 4. Consider the function g(x) = I +3 a) Find the derivative of g using differentiation rules. b)…

A:

Q: 2. Using the limit definition of the derivative, find the derivative of the function %3D 2+1 at z =…

A:

Q: What is the derivative of f(x) · g (x) in terms of f g? -1 Compute the derivative of -sin(x) · 2x…

A:

Q: 3. i. Find f'(x) if f(x) = 9² + tan='(x²) + In(x® + 2x) + cos I +5*. dy ii. Find dr² at the point…

A:

Q: Find the derivatives of the function f for n = 1, 2, 3, and 4. Use the results to write a general…

A: fx=cosxxn When n=1, fx=cosxx Differentiating with respect to x, we get…

Q: 5. Suppose there exits positive differentiable a(x) and B(x) such that a*(x) – B°(x) = 3, and a'(x)…

A: Given: α3x - β3x = 3                                                    1       α'x          =5βx…

Q: if f(x) = x² √In x² x . find the derivative of this function f'(x A. f'(x) = B. f'(x) = c. f'(x) =…

A:

Q: Using the fact that u(x) = In u(x) – In v(x), In v(x) use the chain rule and the formula for the…

A: lnu(x)v(x)=ln u(x)-ln v(x)Formula:ddxln f(x)=1f(x)f'(x)

Q: (5) Find the local maximum and minimum values of f(r) = 1+3x2 – 2.r using either the First…

A:

Q: 3) (a) Let f(x) = -x²-x. Use definition of the derivative Equation 3.4 to compute f'(x). (No other…

A:

Q: (a) Let f(x)=√√2x+1. Use definition of the derivative Equation 3.4 to compute f'(x). (No other…

A:

Q: If F(x) is a differentiable function with derivative F'(x)= Enx"-1 and F(0)=0, then F n=2 x2-x O 1-x…

A: Introduction: For a differentiable function fx, if f'x is given, then integrating both sides, fx can…

Q: Let y = (3x + 2 sin(x)). Find f(x) and g(x) so that y = f(g(x)) and compute the derivative using the…

A:

Q: if f(x) = x²√√In x² x . find the derivative of this function f'(x) A. f'(x) = B. f'(x) = c. f'(x) =…

A:

Q: 1. Determine the true error and relative true error when approximating the derivative of f(x) = -x²…

A: Since there are multiple question, we solve the first one. Post the question again and mention the…

Q: 2 6. Consider f(x) x + 1 a. Find f'(x) using the formal definition of the derivative. b. Find the…

A: Solve the function

Q: Find the derivative of the function f(x) = 4x2 – 13x – 30 by definition of derivatives f(x + h) –…

A: We have to find the derivative of the given function: fx=4x2-13x-30 by the definition of…

Q: A cardboard box manufacturer wishes to make open boxes from rectangular pieces of cardboard with…

A: Given problem:- A cardboard box manufacturer wishes to make open boxes from rectangular pieces of…

Q: 1) Use the Product Rule or the Quotient Rule to find the derivative of the given function a – g(x) =…

A: The objective is to use the product rule or quotient rule to find the derivative of the given…

Q: Using the fact that In[u(x)v(x)] = In u(x) + In v(x), use the chain rule and the formula for the…

A: Given: lnuxvx=lnux+lnvxddxlnx=1x

Q: 2 a) Let f(x) =: Use the definition of the derivative to find f'(0). x+1 b) Let f(x) = Use the…

A: a) Given. The function f(x)=2x+1 The definition of the derivative: The derivative of the function…

Q: 4. Find all derivatives of f(x) = x*, where k is some unknown natural number.

A: f(x) = xk and we need to find all the derivatives of f(x)

Q: 1 Let f(x) 4+ x -1 (a) Using the definition of derivative, show that f'(x) (No points if the…

A: the definition of the derivative is given by . the given function is  substitute x+h for x

Q: Solve for the derivative of the given functions using the Chain Rule formula.Let g(x) = sin (cos…

A: Since, g(x)=sin (cos x)g'(x)=cos (cos x)ddxcos (x)⇒g'(x)=cos (cos x)(-sin (x))ddx(x)⇒g'(x)=-cos (cos…

Q: Find the derivatives of the function f for n = 1, 2, 3, and 4. Use the results to write a general…

A: Given:fx=cos xxn for n=1,2,3,4Formula:ddxuv=vu'-uv'v2

Q: 32. Using one-sided derivatives, show that the function f(4) = { 3x, x>1 does not have a derivative…

A: Given: fx=x3,   x≤13x,   x>1 To Find: To show that the given function does not have a derivative…

Q: (b) If r is an R– R² function and f an R² – R function. State the General Chain rule for determining…

A:

Q: 1 Let f(x) X - 1 (a) Find the derivative f 'of f. 1 f '(x) = (x – 1) X* (b) Find an equation of the…

A:

Q: Let g be a function that has derivative x(x – 3) (x – 5)e2" g'(x) = Does x=3 belong to a local…

A:

Q: Let f(x) =x. cos(x2). What is the correct result of the derivative of f with respect to x? =X•COS…

A:

Q: 1. Find the derivative of f(x) = x² – 3x. Use the result to find the slope of the tangent line to…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: 2. Let x² sin () if x + 0 g(x) = if x = 0. Is g differentiable at 0? If so, find g'(0). Justify your…

A: Given: gx=x2 sin1x,       if x≠00,     if x=0 To Find: Is g differentiable at x=0? If so, to find…

Q: Q. 2. a) Find nth order derivative of f(x) = In(2x-7). b) Find 3rd order derivative of y with…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: