JEE MATHEMATICS MCQ: DIFFERENTIATION

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Application +4 | -1

f:(0, \infty) \rightarrow \mathbb{R}

is continuous. If

F(x)

is a differentiable function such that

F^{\prime}(x)=f(x) \forall x>0

and

F\left(x^2\right)=x^2+x^3

, then

f(4)

equals

View answer and explanation

Correct option: C

Option C (4) is correct because by differentiating F(x²) and using F'(x) = f(x), we can solve for f(4).

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f(x)=|x|^{|\tan x|}

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x

y

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x y=1

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[x]

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x=k, k

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y = {\sec ^{ - 1}}\left[ {\mathrm{cosec}x} \right] + \mathrm{cose}{\mathrm{c}^{ - 1}}\left[ {\sec x} \right] + {\sin ^{ - 1}}[\cos x] + {\cos ^{ - 1}}[\sin x],

\frac{{dy}}{{dx}}

\frac{d}{d x} \sin ^{-1}\left(3 x-4 x^{3}\right)

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v\frac{{\partial z}}{{\partial x}} + \frac{{\partial z}}{{\partial y}}