JEE MATHEMATICS MCQ: DIFFERENTIATION

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Application +4 | -1

f'\left( x \right) = \sin (\log x)

and

y = f\left( {\frac{{2x + 3}}{{3 - 2x}}} \right)

, then

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

x = 1

is equal to

View answer and explanation

Correct option: C

12\sin \log \left( 5 \right)

Option C (

12\sin \log ( 5 )

) is correct because it is the result of applying the chain rule and evaluating the derivative at x=1.

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

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x

y

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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}}