JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

1 of 1

Application +4 | -1

Let

f

be a differentiable function satisfying

[f(x)]^n=f(n x)

for all

x \in R

.
Then,

f^{\prime}(x) f(n x)

equals

View answer and explanation

Correct option: C

f(x) f^{\prime}(n x)

Option C (

f(x) f^{\prime}(n x)

) is correct because, after differentiating the given equation and manipulating the result, we find that

f^{\prime}(x) f(n x) = f(x) f^{\prime}(n x)

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

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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}}