Recall, for a given function f(x), an antiderivative is a function F(x) where F'(x) = f(x) F(x): f(x)dx. or For each of the following functions, find an antiderivative with the help of the Reverse Power Rule: (a) f(x) = x² +1 (b) f(x) = V – 2a° (c) f(x)= x1.3 + 7x2.5 (d) f(x) = (1– x²)² [Hint: Expand the bracket]

Q: Find f (x) if f'(x) = 3x² + 4x + 1 and f (2) = 21. f (x)

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Q: Differentiate the following with respect to x: f(x) = x³In (x)

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Q: Let f (x) = Evaluate the following. Simplify if possible. 9x +7 f (x) – f(a) a) 7 where A = A' for x…

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Q: If f(x)=V x + Vx , find the value of f(1) (a) 3/2 (b) 8. (c) 4 (d) 1 (e)

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Q: Explain why

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Q: Let h(x)=f(x)/g(x). If f(x)=−cos(x) and g(x)=4x^2+2x−3, what is h′(x)?

A: Given,          hx=fxgx. And fx=-cosx  and  gx=4x2+2x-3.

Q: Find the derivative of the following functions a) f(x) = 1 + x² + = 160 1x x6 I b) F(X) x4-3x+1 √x…

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Q: Determine f(x) given that f'(x) = 12x2 – 4x and f(-3) = 17

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Q: Let f(z) = 11 – z f (z) =

A: To write the inverse of the function y = f(x), we need to rewrite the terms such that we could write…

Q: 1. Differentiate the following f(x) = (2x) (e4x)

A: f(x)= 2xe4x Find f'(x)

Q: Let f(x) = xV*. Find f'(9).

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Q: find a function f for x>0 so that f(x,y)=yf(x)+yf(x)

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Q: Find the general form of f if f'(x)= 9f(x). f(x) = ]

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Q: Find the general form of f if f'(x) = 5f(x).

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Q: Consider the following functions: f(x)= x+1' and g(x) = Find the domain of (f og)(x). Enter your…

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Q: Find f. f "(x) = 1//1- x?, () - = 2 f(x) =

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Q: 1 For the function f (x) = 2 (x + 4) – 6, find f(x).

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