Differentiation of Different Type of Functions

Suppose $f\left(x\right)=\tan \left({\sin }^{-1}\left(2x\right)\right)$, then $f^{\text{'}}\left(\frac{1}{4}\right)$ is equal to

Differentiate $\sin 2x$

Find the derivative of $\cos 3x$

If $x=a{\cos }^3\theta$ and $y=a{\sin }^3\theta$,

Then find $\frac{dy}{dx}$

Let $f\left(x\right)=\frac{\sin x+\cos -\sqrt{2}}{\sin x-\cos x},x\in \left[0, \pi \right]-\left\{\frac{\pi }{4}\right\}$, then $f\left(\frac{7\pi }{12}\right)f^{"}\left(\frac{7\pi }{12}\right)$ is equal to

Evaluate: $\frac{d}{dx}\left(\sqrt{\frac{1-\cos 2x}{1+\cos 2x}}\right)$

If $y={\left(secx\right)}^x+{\left(\log x\right)}^{\sqrt{x}}$ then find $\frac{dy}{dx}$

If $f\left(x\right)={\log }_e\tan \left(\frac{\mathrm{\pi }}{4}+\frac{x}{2}\right)$ prove that $f\text{'}\left(x\right)=secx$

If $\mathrm{y}=\mathrm{cosec}\left(\cot \sqrt{\mathrm{x}}\right)$ then find $\frac{dy}{dx}$.

$\frac{d}{dx}cot(\log x)$

Differentiate $y={\left(\sin x\right)}^x+x\log x$ w.r.t. $x.$

If $y=\frac{\cos 6x+6\cos 4x+15\cos 2x+10}{\cos 5x+5\cos 3x+10\cos x}$, then $\frac{dy}{dx}=$

If $f\left(x\right)=\sin \left(\frac{\mathrm{\pi }}{3}\left[x\right]-x^2\right), 2<x<3$, where $\left[·\right]$ is the greatest integer function, then $f^{\text{'}}\left(\sqrt{\frac{\mathrm{\pi }}{3}}\right)$ equals.

If $y=\cos 2x·\cos 4x·\cos 8x$ then $\frac{dy}{dx}=$

If $y=\log \left(\tan \left(\frac{x}{2}\right)\right)+{\sin }^{-1}\left(\cos x\right)$ then $\frac{dy}{dx}$ is

Differentiate $\sin ²(3x+4)$

Find the derivative of $x\sin x$

If $x=a{\cos }^3\theta$ and $y=a{\sin }^3\theta$, prove that $\frac{dy}{dx}=-{\left(\frac{y}{x}\right)}^{\frac{1}{3}}$

Find the value of $\int \frac{dx}{\left(1+x^2\right)\sqrt{{\tan }^{-1}x+4}}$