If $f\left( x \right)$ and $g\left( x \right)$ are two functions with $g\left( x \right) = x - \frac{1}{x}$ and $fo{\rm{g}}\left( x \right) = {x^3} - \frac{1}{{{x^3}}},$ then $f'\left( x \right)$ is

JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

1 of 1

Analyzing +4 | -1

f\left( x \right)

and

g\left( x \right)

are two functions with

g\left( x \right) = x - \frac{1}{x}

and

fo\mathrm{g}\left( x \right) = {x^3} - \frac{1}{{{x^3}}},

then

f'\left( x \right)

View answer and explanation

Correct option: A

3{x^2} + 3

Option A (

3{x^2} + 3

) is correct because by substituting

g(x)

into

f(g(x))

and simplifying, we find

f(x) = x^3 + 3x

, and thus

f'(x) = 3x^2 + 3

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