Which of the following is true about the derivatives of differentiable functions f an d da (2) – 9(x)] = gʻ(x) – f'(x) (A d [f(x) f'(x) gʻ(x) • 9'(x) # 0 dx d d f(x) + g(x)] = f'(x) +g'(x) d [f(r): alr)1. f'(r): a' (r)

Q: h(x) = f(gx)) calculate the following derivatives using the table a) h'(3) b) h'(2)

A: Given

Q: 2. (a) Find the derivative of f(x) = 2x2 – 2x + 2 from first principle sin x (b) If y = x + find x4…

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Q: Let h(x) = f(g(x)) and p(x) = g(f(x)). Use the table below to compute the following derivatives. a.…

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Q: 2 a) For the function f(x) = X-3 , find f'(1) by using the definition of derivative.

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Q: Consider the function. f(x) = x R(x) + Q(x) Identify the derivative f'(x). f'(x) = xR'(x) + R(x) +…

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Q: In(3x) Given f(x) the derivative f'(x) is 3 1 3x 1 3x 3 3

A: f(X) = ln(3x)/3

Q: Consider the function. y = 5x Let f(u) = 5". Find g(x) such that y = f(g(x)). u = g(x) = Find f'(u)…

A: Given Y = 5x². Y = 5x² f(u) = 5u G(x) is also a function Y = f(g(x))

Q: Make a sign diagram for the derivative of the function. f(x) = x² + 4x³8x² + 52 f'(x) ? 0 f'(x) ?0 X…

A: The given function is

Q: let f(x) be a function such that its derivative is given by: f'(x)=5(x-1)^2(x-2)^3(x-3)^4. which…

A: Consider the graph of given first derivative: If the graph of f '(x) changes from negative to…

Q: Find the derivative of the function f(z) = 6z² – 18z by the definition of derivatives f'(z) = lim…

A: f(x)=6x2-18x

Q: Let h(x) = f(g(x)) and p(x) = g(f(x)). Use the table to compute the following derivatives. a. h'(4)…

A: In loose transaction of composite function u(v(x)), v is known as inside function and u is known as…

Q: Let g(x) = 2 f(u) + 3 where . u = x² + 2x. What is the derivative of g with respect to x? ○ 2. f'…

A: Given that, the function is gx=2·fu+3 and u=x2+2x. By the chain rule formula ddtFut=F'ut·u't.

Q: How many non-zero derivatives does f(x) = 3x³ + 7x² 9 have? Find all non-zero derivatives: f'(x) =…

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Q: Find the indicated derivative for y=f(x)=9-x^2

A: Answer and explanation is given below...

Q: The table below gives values of the function values and derivatives of f(x) and g(x) f(x) a) Given…

A: x f(x) f'(x) g(x) g'(x) 1 3 -1 2 -1 2 2 -1 1 0 3 1 -1 2 1

Q: Evaluate the derivative of y = (x 2+ 2x + 1)2usingd/dx (ƒ(g(x)) = ƒ′(g(x)) # g′(x)

A: We have to evaluate the derivative ofy = (x2+ 2x + 1)2usingddx(f(g(x))=f'(g(x))*g'(x)

Q: Compute the derivative of g(x) = cos(t) dt-

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Q: 2) a) Let f(x) = 2* + 3x7. Find f'(x) and f" (x). b) Find the derivative f'(x) in the following…

A: a.)   Given f(x) = 2x + 3x-1/2 f'(x) , f''(x) are to be calculated. Formulas used here  ** y = ax…

Q: (

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Q: Find the derivative of f(x) = (10z (1026 + =2 – 1)° f' (z) =

A: Given function

Q: Find the derivative of f(#) v5-tan(r)

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Q: The first derivative of a continuous function y = f(x) is y' = x(x - 9)². Find y' and then use the…

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Q: Let F(x) = sin(x) ex a) Find f'(x), F"(x), f (³) (x), F"" (x) b) Find f (2) (x), the 2n-th…

A: Here, we have to find the derivatives of f(x)=sin(x)exWe shall be using the product rule of…

Q: f2(x) = (4x + 5)°, f3(x) = (2x² + x)/x, fa(x) = cos(3x) – 2 sin² x,

A: As this is a multiple subpart question according to the Bartleby Answering rule, only first three…

Q: Use the definition of derivative to find f'(x) and f"(x) f(x) = 4x² + 3x + 2 f'(x) =

A: