If ${x^y}.{y^x} = 16$, then the value of $\frac{{dy}}{{dx}}$ at (2,2) is

JEE MATHEMATICS MCQ: DIFFERENTIATION

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Application +4 | -1

{x^y}.{y^x} = 16

, then the value of

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

at (2,2) is

View answer and explanation

Correct option: A

- 1

Option A (- 1) is correct because after taking the logarithm and differentiating implicitly, the derivative at the point (2, 2) is -1.

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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}}