Suppose that the functions f and g and their derivatives with respect to x have the following values at the given values of x. Find the derivative with respect to x of the given combination at the given value of x. x|f(x) g(x) f '(x) g (x) 3 1 16 4 -3 3 3 4 f(x) · g(x), x = 3 48 131 35 259

Q: 89. Suppose that functions f and g and their derivatives with respect to x have the following values…

A: * As per our guidelines, we are supposed to solve only the first three problems/subdivisions. Please…

Q: Give the derivative formula for the function. j(x) 4 In x e5 = j(x)

A: The function is given by,

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

A:

Q: Find the first derivative of y with respect to x (y') of the given function using rules for…

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: 2. Find the derivative of the following functions. (a). g(x) = cos (2x + 1) (b)," f(x) = In (x² – 4)…

A: To find the derivative of the functions

Q: Suppose that the function ƒ(x) and its first derivative have the followingvalues at x = 0 and x =…

A:

Q: 1. Find the derivative of f(x)= x(a+1), given a is a constant.

A:

Q: If f(x)=In(x-1), find the formula for f^((n))(x), the nth derivative of function f(x) f(x) = ln (x –…

A:

Q: 4. Find the derivatives with respect to x of the function 2 – 3x^2. 5. Differentiate ax² + b to the…

A: Using derivative of composite function.

Q: 1. Find the derivative of the following function: f(x) : (x² sin- if x ± 0 if x = 0

A:

Q: 2ƒ(x), x = 2

A:

Q: 2. Find the derivative of the following functions: (5x+ 1)'(x + 3)5 cos°(x) sin°(x) (a.) f(x) = .…

A: Given f(x)=5x+77x2+35cos2x sin3x3   As per our guidelines we are supposed to answer only first…

Q: Find the derivative of the following. 2. g(x) = sin x tan x 1+sin x 3. h(x) = 1-sin x x+4 4. i(x) =…

A: 2.g(x)=sinx tanx3.h(x)=1+sinx1-sinx4.i(x)=x+4cosx5.j(x)=[(x2+cosx)(2x-sinx)]

Q: 1. Compute the first, second, and third derivative of a. f(x) = x² In(x+ 1)

A:

Q: *(x) = x² +x – 7 , find f'(a) at a = -2 by using the definition of derivative.

A: To find the f'(a) using definition of derivative

Q: Find the finite derivative of a the functions below at x=1: a) f(x) = 4x³-3x²+2x-3 3 b) f(x)==-²/ 3…

A: Concept: The derivative can be represented as f'(x) or ddx(f(x)) Derivative of xn: ddx(xn)=nxn-1…

Q: Suppose that the function ƒ(x) and its first derivative have the followingvalues at x = 0 and x =…

A: Given that: The function f(x) and its first derivative have the following values at x = 0 and x = 1.…

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: 5 .Let f(x) =x² -e*. Find the value of x for which the second derivative s"»equals zero. 2

A:

Q: Suppose that the functions f and g and their derivatives with respect to x have the following values…

A:

Q: find the derivative of the following: f(x) = e^x (2x^2-x+3)

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: Let f (x) =x. cos(x2). what is the correct result of the derivative of f with respect to x? A…

A:

Q: Let f be the function defined for x > 0, with f (e) = 2 and f', the first derivative of f , given by…

A: Given, f be a function defined for x>0 and the derivative of f is f'x=x2lnx Point e, 2

Q: Suppose that the functions f and g and their derivatives with respect to x have the following values…

A:

Q: 59. Suppose that functions f and g and their derivatives with respect to x have the following values…

A: Since you have posted multiple questions i can do first question with first three subparts as per…

Q: Suppose that the functions f and g and their derivatives with respect to x have the following values…

A: Given : 1g2x

Q: 6. Suppose that f(x) = g(y) + x²y³ r + y (a) Use implicit differentiation to compute a formula for y…

A: We differentiate above function with respect to x and f(x) and  g(x) are function of x and y

Q: 8. y (1 + x³)(3 – 2x) 10. y = (x2 + 3)(x² – x + 1

A:

Q: We are given that the derivative of f is f′(x)=3x2−12x−15 and that f(1)=81.   The absolute maximum…

A: We are given that the derivative of f is f′(x)=3x2−12x−15 and that f(1)=81.   The absolute maximum…

Q: f(x) = x2 -1

A:

Q: Which of the following is the derivative of the function f (x) = 5x · e*? Of (x) = 5e* Of'(x) = 5e*…

A:

Q: 2. Given f(x) = x³ – 2x² + x + 2, find x e (-1, 3) such that f'(x) = 5. 3. Compute the derivative of…

A: Since you have posted multiple questions, as per our guidelines we are allowed to answer the first…

Q: 1. Compute the first, second, and third derivative of a. f(x) = x² In(x+1) b. h(x) = x² sin x

A:

Q: What is the first derivative with respect to x of the function g(x) = 3/9x O 1/2 9.

A:

Q: Suppose that the functions f and g and their derivatives with respect to x have the following values…

A: x      f(x)    g(x)     f1(x)    g1(x)      3      1      4      6     3      4…

Q: Solve for the derivative of the given functions using the Chain Rule formula. Suppose f(x) =…

A: Given, f(x)=sin(2x)+17

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: A2) Find the derivative of the following functions: x² + 4 (a). f(x) x2 - 4 (b). f(x) = 2 tan-'(x) –…

A:

Q: (a) f(x) = (3x² – 5x + 8)35 (b) f(x) = cos(27.x)

A: First I have written the chain rule and then using it find the derivative of given functions.Also…

Q: Give the derivative formula for the function. (x)2 In x -e j'(x)

A: Consider the given function.

Q: 2. Find the first derivative of the following expression: f(x) = (x2 + 1)sin a

A: take derivative  use the exponent rule

Q: 11.Find the derivative of the functions: a) f(x) = In(9x²2 – 3x) b) g(x) = In(ln x)

A:

Q: Let the function y(x) be given implicitly via the equation xy – In y = 2. Determine the value of its…

A:

Q: 1. Find the derivatives of the following functions: a. g(x) = x ÷ sin(x). 2. Find the derivative…

A: Find the derivatives of the following functions:  a. g(x) = x ÷ sin(x). 2. Find the derivative of…

Q: Find the derivative with respect to x of h(x) = e2x²+6 In(x).

A:

Q: Suppose u and v are differentiable functions of x. Use the given values of the functions and their…

A: Given:

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: Let f (x) = x sin x and g(x) = x cos x. (a) Show that f ,(x) = g(x) + sin x and g ,(x) = −f (x) +…

A: