Assume that f'(4) = − 2, g'(1) = At x = 1, y' = (Simplify your answer.) g(1) = 4, and y = f(g(x)). What is y' at x = 1? 9'

Q: Find y'' in y = x2 (x3 - 1)5

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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: Given f''(x) = - 16 sin(4x) and f'(0) Find f ¹ƒ(3/3) = = 6 and f(0) = - 5.

A: SOLUTION-

Q: Use the figure below to calculate the derivative, g' (7) if g (x) = f¬1 (x). (2.1,7.4), f(x) (2 ,7 )…

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Q: Given g(x) = 2x² + 6 what is g'(38) ? %3D

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Q: Find f'(x), f''(x), and f (x) for the following function. f(x) = 9x° + 5x2 + 8x %3D

A: differentiate wrt to x

Q: 3. Evaluate the derivatives of the following: i. 2t +3 ii. x' sin x iii. In(3x-4) iv. (2x +5)"

A: i. Quotient Rule:  The Quotient Rule for differentiation is given by, Evaluate the derivative of…

Q: • y= cos(a' + x')

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Q: If f(x) = 8 sin '(x²), find f'(x). Find f'(0.6).

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Q: x² find f''(x). Then find f''(0) and f''(9). For the function f(x) = %3D 9 + x

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Q: Find y'' in y = (1 + 1/x)3

A: We first expand the given expression first.

Q: 1 Assume that f'(4) = -5, g'(2), g(2)=4, and y=f(g(x)). What is y' at x = 2? 8 Atx=2, y'= (Simplify…

A: The chain rule of differentiation is given by

Q: 7. Find y' for y = (sinx)*.

A: The given function is y=(sin x)x. Rewrite the given function as follows.

Q: Find f'(0) if f (x) = In(cos .x).

A: we have to find f'(0)

Q: If f(x) = cos x, then f'() = A. B. - C. - C. D. √3

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Q: Let f(x) = 5x4 - -1/2+8√x-3. (a) Find f'(x). (b) Find an equation for the tangent line to the graph…

A: Given that            function f(x) = 5x4-2x2+8x-3     Now             f'(x)    =  ddx5x4-2x2+8x-3…

Q: x2 find f"(x). Then find f"(0) and f''(7). For the function f(x) = %3D 3 + x' f"(x) =

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Q: For each problem, find the function f based on the information given. 13. f'(x)=√x(6+5x) 14.…

A: 13) Given:  f'(x) = x6+5x ⇒f'(x) = 6x12+5x32 Integrate both sides with respect to x we get

Q: Find g' (6) given that f(6) = - 3 and f' (6) = 6. Enter the exact answers. (a) g(x) = 7x² – 6f (x)…

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Q: Find g'(4) given that ƒ(4) = 7, ƒ'(4) = −1, and g(x) = √xƒ(x). Answer:

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Q: Suppose that f(4) = 2 and f' (4) = h(x) = (2x² + 3in (f(x)))² h' (4) = (b) h(x) = 20f(x) e-2x + 3…

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Q: Given f''(x) = - 25 sin(5x) and f'(0) = 2 and f(0) = -6. Find f() =

A: In this question, we want to compute the value of f at the given point.

Q: Suppose that f(4) = 2 and f' (4) = -1. (a) h(x) = (2x². 2x² + 31n (f(x)) h'(4) = (b) h(x) = 20f(x)…

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Q: Given f''(x) = ƒ(5) Find f = S 9 sin (3x) and f'(0) - 4 and f(0) = 1.

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Q: For the function f(x) = f'(x) = 0 x² 1+x find f''(x). Then find f''(0) and f''(8). 1

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