3. Suppose that {f(t)} = F(s) with F a differentiable function and that L{f'(t)} Exists. Then L{-te¹2t f'(t)} is equal to:

Q: Evaluate the double line integral S  of the fuinction (x − 2y + z) dS. S: z = 9 − x,  0 ≤ x ≤ 9,  0…

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

A:

Q: 9) Determine the third derivative with respect to x for y = In x 10) Given f(x) 2x + 1 and f(1) 4.…

A: Find the derivative

Q: 2. Use the definition of derivative to find the derivative for f(x) = x2 + 3x . | f(x +h) – f(x) lim…

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Q: Let f(z) ==+[=] Find f'(2). x+ [c]*

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Q: Suppose f and g are functions that are differentiable at x=5 and that f(5)=8 ,f'(5)=-3 ,g(5)=-1 ,…

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Q: 1. Sketch a function f(x) with the following properties: • f'(x) > 0 and f"(x) = 0, for x 2

A: As you posted multiple question , I need to solve only first question.

Q: Let f and g be functions satisfying that f(1) = 3, g(1) = 4, f'(1) = 1, g'(1) = 5. For the following…

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Q: Let H(x) = f(xg(x)), where f and g are differentiable functions such that g(2) = 3, g' (2) = 5, and…

A: We will solve the following.

Q: Find the derivative of the function f(x) = 3x2- 13x 25 by definition of derivatives f(x + h) - f(x)…

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: 2 Assume that f'(2) = -9, g'(3) = g(3)=2, and y=f(g(x)). What is y' at x = 3?

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Q: 2. f"(x)=3sin x, f'(0)=1, and f (0)=10. Determine f(x).

A:

Q: 1’) Let f be the function f(x) = x^2 +36/x^2 (a) Calculate f'(x) and find all stationary points for…

A: Solution - Given function - f(x)=x2+36x2 a.)        f'(x)=2x+36-2x-2+1             f'(x)=2x-72x…

Q: (a) Sketch the dependency diagram for w = f(x, y, z) = 3.xyz – y²z, with x = 2t + s, y = -t – s, z =…

A:

Q: 7. Determine f'(x) where

A: Derivative: - The rate of change of a function with respect to a variable is called derivative in…

Q: Suppose that f and g are functions such that (0) = 4, f'(0) = 5, g(0) = –2, gʻ(0) = 3. %3D æf(x)…

A:

Q: Find f' in terms of g' if (i) f(x) = g(x + g(a)). %3D

A: We will use the formula f(g(x))' = f'(g(x))g'(x)

Q: Suppose that f and g are differentiable functions such that f (0) =2. f'(0) =-5. g (0) =- 3. and…

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Q: Given f (x) = x³ - 3x – 1,x 2 2, find (f~')'(-1)

A: