4, Differentiate the function. (3) f(x)= In 2.x²(x+2)³ (3х - 2)5 (4) f(x)=In, |(x+1)(x+2) x(х — 1) 5, Find y' and y". (2) f(x)= log,0 *

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Given: fx=2x−1x2+3x2+1, and gx=x2+872−3x25 To check whether: f'x=4x2x2−1+2xx2+3−2xx2+12x2−1x2+3x2+1,…

Q: Suppose that f(2) = -4, g(2) = 5, f '(2) = -1, and g'(2) = 2. Find h'(2). (a) h(x) = 3f(x) – 5g(x)…

A: Since, you have asked multiple parts in a single question, we would be answering only the first…

Q: 1 Po(x) = v2 3 P1(1) = : %3D "V 2 PĄ(2) = (3=² – 1) V P3(x) = ; (5x³ – 3r) /5 Write down the…

A: We will find out the required values.

Q: 1.2 s Find first derivative for the following functions. dx (a) y = 5+ 6x + 4x3 (b) y = In(2x) +x*…

A: Note:-Since you have asked multiple questions, we will solve the first question with three sub-parts…

Q: Let ƒ (x) = x³ – 5x² – 8 and let g be the inverse of f (i.e. g (x) = f -1 (x).

A:

Q: Determine h(1) and h'(1). h(x) = [f (x)]2

A: The function h(x) is a composite function since its input is another function f(x). Now h(x)=[f(x)]2…

Q: Let f(x): V (x+4)6(2x - 1) (4x + 4)4

A:

Q: If f(x) = log,(cot(x) + a?) , then f'(x) = %3D (A) 1 (cot(x)+2?) (B) csc (x)+2x (cot(x)+r) 1 (C)…

A: By using differentiation formula and change of basis formula, we calculate the derivative of given…

Q: If f and g are functions that satisfy f'(2) = -3 and g'(2) = -1, find h'(2) for h(x) = -5f(x) +…

A:

Q: 4. Find the derivative. x? + 6x – 5 (a) 5х -1 (b) ƒ(x) = (3xr² – 5x - 7)' Us e chain rule (c) y =(x-…

A: Topic:- derivatives

Q: Determine h(1) and h'(1). h(x) = f (x) / g (x)

A: Value of the function is , the value of combined function, when variable is replaced with that…

Q: Suppose g(x)= 3 2(1–5x)3 k (1–5x)4' with a derivative g'(x) = - " for some real number k. What is…

A:

Q: If f and g are functions that satisfy f'(2) = 5 and g'(2) = −2, find h'(2) for h(x) = 2f(x) - g(x) +…

A:

Q: A) Differentiate y = 4Vx +- + 10 8 B) Find the second derivative of y = 4Vã + + 10 C) Find the…

A: As per our guidelines  we can solve only  3 subparts of a question . The rest can be reposted.  In…

Q: Let f(x) and g(x) be functions whose graphs are shown below. Which of the following statements…

A: We are asked about the derivative of the function h given a graph of the functions f and g. Note…

Q: (a) -3r*, (b) x* + 4r3 + 6x2 + 4x + 1, (c) Ar10 + bx+c (A, B and C are constants).

A:

Q: Determine whether the functionf is one-to-one by examining the sign of f' (x). (a)ƒ(x) = x³ + 9x2 –…

A:

Q: Find f'(x) and simplify. f(x)= Which of the following shows the correct application of the quotient…

A:

Q: Suppose g and h are functions such that g (x) = ln (1 + h (sqrtx)). Find g'(4), given that h'(2) = 1…

A:

Q: A table of values for f, g, f', and g' is given. f(x) g(x) 3 2 1 8 7 2 X 1 2 3 (a) If h(x) =…

A: A table of values for f, g, f', and g' is given. x fx gx f'x g'x 1 3 2 4 6 2 1 8 5 7 3 7 2…

Q: - 3. Use product rule to find the derivative of the following fur (a) f(x) = 3e5. ln(2x² − 3x +π).…

A: according to bartleby guide line we supposed to do only first part of multiple questions. (a)  given…

Q: Find each of the following. In some cases, you may need to rewrite the function firs (a) F'(x) for…

A:

Q: Q) Plot, on the same figure, three related functions of y1 = log(x) and y2 = sin(x-.2), in the…

A: The figure can be made using geogebra or desmos. First Plot the function y=logx as shown:

Q: Q3: find the derivative of In(x4+3x-1) a) f(x) = %3D x²+1 b) f(x) = 4x³ . log(x² + 2x) %3D c) f(x) =…

A: Use product rule of differentiation.

Q: y = (x+6)(x+8)® (x+3)³(x+5)5 Differentiate using Logarithmic Differentiation

A: