In this question, the function f is differentiable, and f' (x) = g(x). We don't know exactly what f(x) or g(x) are, so your answers will have f(x) and g(x) in them. Compute the derivatives of the following functions. (a) (x + f(x))2º (b) In(x² f(x)) (c) esia(f(x))

Q: (2) Find the derivative of each of the following functions (a) f(x) = (1+x*)²/3 (b) g(x) = V1+…

A: a) We use the power rule and chain rule

Q: +² 2+x If f(x): f*(4) = 1/8 find f"(4).

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Q: Write down the equation of any function g(x) for which the derivative does not exist at x =2.

A: Topic = Derivative

Q: If f(x) - g(x) = 1, then f and g have the same derivative. O True O False

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Q: Consider the following functions. g(x) = x3 – x h(x) = (x3 – x)4 f(x) = 9(x3 – x)4 Find the…

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Q: If a function y(x) can be expressed as the ratio cg(x) + G(x) cf(x) + F(x) y = where c is a constant…

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Q: Complete the table by finding the function g(x) and the derivative of g(x) and h(x), if possible.…

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Q: If a function is defined by an equation G(x,y)=0 and could be found explicitly as y=f(x), then the…

A: We have to check

Q: 2. Find the anti-derivative of a. f(x) = 2x¹ - 5√√x³7−2e* ++ 3 1 1+x²

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Use the given information to find f '(4). f(x) = g(x)h(x) g(4) = 9 and g'(4) = -5 h(4) = -7 and…

A: Will differentiate the given function with respect to X using the product rule and then substitute x…

Q: By considering the first two derivatives of g(x), show for x > 0: ex>1+x-x²

A: According to question,Given function,g(x) = ex - 1 - x + x2

Q: 2x 1) Calculate the derivative of h(x) = √√e²x +e-²x

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Q: Find the derivative of the following: a.) f(x) = 5x6 +- 3x3/5 x3 b.) f(x) = (x' + 4x)(x5 – 2) (Hint:…

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Q: For f(x) = -6x² + 3x + 2, find f'(x) using the Definition of the Derivative. (Note: This is the one…

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Q: 5. If f(x) = x², g(x) = and h(x) = √x² + 2x, determine the derivative of each composite function. a.…

A: Given: f(x)=x2,g(x)=1x′ and h(x)=x2+2x First find the composite functions and then differentiate