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JEE MATHEMATICS MCQ: DIFFERENTIATION

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Application +4 | -1

If

f(x)

and

g(x)

are two functions from

\mathbb{R}

to

\mathbb{R}

such that

(f \circ g)(x)=\left(x^3-x^2+2\right)^8

, then

f^{\prime}(1) g^{\prime}(1)

is

View answer and explanation

Correct option: A

8

Option A (8) is correct because, by choosing

f(x) = x^8

and

g(x) = x^3 - x^2 + 2

, we get

(f \circ g)(x) = (x^3 - x^2 + 2)^8

. Then,

f'(1) = 8

and

g'(1) = 1

, so

f'(1)g'(1) = 8

.

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