JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Medium

1 of 1

Application +4 | -1

A differentiable function

f\left( x \right)

is defined for all

x > 0

and satisfies

f\left( {{x^3}} \right) = 4{x^4}

for all

x > 0.

The value of

f'\left( 8 \right)

View answer and explanation

Correct option: B

\frac{{32}}{3}

Option B (

\frac{{32}}{3}

) is correct because it is the value of the derivative

f'(8)

obtained by differentiating the given function

f(x^3) = 4x^4

and substituting

x=2

More Questions from DIFFERENTIATION

Practice All Chapter MCQs →

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

f^{\prime}\left(\frac{-\pi}{6}\right)

x

y

x>0

x y=1

x+y

f(x)=[x] \sin (\pi x)

[x]

x

x=k, k

f(x)

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)

z = y + f\left( v \right),

v = \left( {\frac{x}{y}} \right),

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