List of top Mathematics Questions on Derivatives of Functions in Parametric Forms asked in KEAM

If \( x^3=\sin\theta,\ y^3=\cos\theta \), then \( x\dfrac{dy}{dx} \) is

If $y=\sin x\sin 2x$ and $t=\cos x$, then $\frac{dy}{dt}$ is:

If $u=\sec^{-1}(-\sec 2\theta)$ and $v=\cos \theta$, then $\frac{du}{dv}$ at $\theta=\frac{\pi}{4}$ is equal to:

If $x = \frac{3t}{1+t^3}$ and $y = \frac{3t^2}{1+t^3}$, then $\frac{dy}{dx}$ at $t=1$ equals

If \( x = 2\cos t - \cos 2t \) and \( y = 2\sin t - \sin 2t \), then \( \frac{dy}{dx} \) at \( t = \frac{\pi}{2} \) is

If $s = \sec^{-1} \left( \frac{1}{2x^2 - 1} \right)$ and $t = \sqrt{1 - x^2}$, then $\frac{ds}{dt}$ at $x = \frac{1}{2}$ is:

If \( |t|<1 \), \( \sin x = \frac{2t}{1+t^2} \), \( \tan y = \frac{2t}{1-t^2} \), then \( \frac{dy}{dx} \) is

If \( x = \sin t \) and \( y = \tan t \), then \( \frac{dy}{dx} = \)

If \( x = a \cos^3 \theta \) and \( y = a \sin^3 \theta \), then \( 1 + \left( \frac{dy}{dx} \right)^2 \) is:

If \( x = a \cos^3 \theta \) and \( y = a \sin^3 \theta \), then \( 1 + \left( \frac{dy}{dx} \right)^2 \) is:

If \( x = \sin t \) and \( y = \tan t \), then \( \frac{dy}{dx} = \)

If \( x = a \cos^3 \theta \) and \( y = a \sin^3 \theta \), then \( 1 + \left( \frac{dy}{dx} \right)^2 \) is:

If \( x = \sin t \) and \( y = \tan t \), then \( \frac{dy}{dx} = \)