If $\sin y + {e^{ - x\cos y}} = e$, then $\frac{{dy}}{{dx}}$ at $\left( {1,\pi } \right)$ is

JEE MATHEMATICS MCQ: DIFFERENTIATION

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Application +4 | -1

\sin y + {e^{ - x\cos y}} = e

, then

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

\left( {1,\pi } \right)

View answer and explanation

Correct option: C

e

Option D (

e

) is correct because after differentiating the given equation implicitly and substituting x=1 and y=

\pi

, the value of

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

is found to be e.

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}}