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

If \( x = at^4 \) and \( y = 2at^2 \), then \( \frac{d^2y}{dx^2} \) is equal to :

If $x = a \cos^3 t$ and $y = a \sin^3 t$, then the value of $\frac{dy}{dx}$ at $t = \frac{\pi}{4}$ is:

If \( x = \sqrt{2^{\text{cosec}^{-1} t}} \) and \( y = \sqrt{2^{\text{sec}^{-1} t}} (|t| \ge 1) \), then dy/dx is equal to :

If $x = \tan^{-1} \left\{ \frac{\sqrt{1+t^2}-1}{t} \right\}, y = \cos^{-1} \left\{ \frac{1-t^2}{1+t^2} \right\}$, then $\frac{dy}{dx}$ is equal to

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 $x = \tan^{-1} \left\{ \frac{\sqrt{1+t^2}-1}{t} \right\}, y = \cos^{-1} \left\{ \frac{1-t^2}{1+t^2} \right\}$, then $\frac{dy}{dx}$ is equal to

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

Differentiate \( \log_a x \) with respect to \( a^x \)

If $x = \tan^{-1} \left\{ \frac{\sqrt{1+t^2}-1}{t} \right\}, y = \cos^{-1} \left\{ \frac{1-t^2}{1+t^2} \right\}$, then $\frac{dy}{dx}$ is equal to

If the lines \( \frac{x-k}{2} = \frac{y+1}{3} = \frac{z-1}{4} \) and \( \frac{x-3}{1} = \frac{y - 9/2}{2} = z/1 \) intersect, then the value of \( k \) is:

If \( 2 \tan^2 \theta - 5 \sec \theta = 1 \) has exactly 7 solutions in the interval \(\left[ 0, \frac{n\pi}{2} \right],\) for the least value of \( n \in \mathbb{N} \) then \(\sum_{k=1}^{n} \frac{k}{2^k}\) is equal to:

Let $x=\sin \left(2 \tan ^{-1} \alpha\right)$ and $y=\sin \left(\frac{1}{2} \tan ^{-1} \frac{4}{3}\right)$ If $S =\left\{\alpha \in R : y ^2=1- x \right\}$, then $\displaystyle\sum_{\alpha \in S } 16 \alpha^3$ is equal to ______

The derivative of $f(\sec x)$ with respect to $g(\tan x)$ at $x=\frac{\pi}{4}$, where $f^{\prime}(\sqrt{2})=4$ and $g^{\prime}(1)=2$, is

If $f'(x) = \sin(\log x)$ and $y = f\left(\frac{2x+3}{3-2x}\right)$, then $\frac{dy}{dx}$ at $x=1$ is

If $x = a(t + \sin t), y = a(1 - \cos t)$, then $\frac{dy}{dx} =$

If $x = a \cos \theta$, $y = b \sin \theta$, then $\left[\frac{d^2 y}{d x^2}\right] = $

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 \( \frac{dy}{dx} = \)