If $x = a{\cos ^4}{\rm{\theta }},y = a{\sin ^4}{\rm{\theta }},$ then $\frac{{dy}}{{dx}}$ at ${\rm{\theta }} = \frac{{3\pi }}{4}$ is

JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Medium

1 of 1

Application +4 | -1

x = a{\cos ^4}\mathrm{\theta },y = a{\sin ^4}\mathrm{\theta },

then

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

\mathrm{\theta } = \frac{{3\pi }}{4}

View answer and explanation

Correct option: A

- 1

Option A (-1) is correct because after finding dy/dx in terms of theta, substituting theta = 3pi/4 yields -1.

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}}