Differentiation using Chain Rule or Substitution

Differentiate:

$(ax+b{)}^n(cx+d{)}^m$

Find the derivative of ${\sin }^{n}x$

If $\frac{dy}{dx}=x^4$, then find $\frac{dx}{dy}$.

If $\frac{dy}{dx}=2x^3$, then find $\frac{dx}{dy}$.

If $\frac{dy}{dx}=x^2$, then find $\frac{dx}{dy}$.

If $\frac{dy}{dx}=2x^3$, then find $\frac{dx}{dy}$.

If $\frac{dy}{dx}=3x^2$, then find $\frac{dx}{dy}$.

Let $f\left(x\right)=x+\mathrm{c}\mathrm{o}\mathrm{s}x+2$ and $g\left(x\right)$ be the inverse function of $f\left(x\right)$, then $g^{\text{'}}\left(3\right)$ is equal to

Suppose, the function $f\left(x\right)-f\left(2x\right)$ has the derivative $5$ at $x=1$ and derivative $7$ at $x=2$, the derivative of the function $f\left(x\right)-f\left(4x\right)$ at $x=1$ has the value $10+\lambda$, then the value of $\lambda$ is equal to:

Differentiate the following functions w.r.t.$x$

$\log \left[\frac{x+\sqrt{x^2+a^2}}{-x+\sqrt{x^2+a^2}}\right]$

Differentiate the following function w.r.t.$x$

$\log \left[{\sin }^{3}x·{\cos }^{4}x·{\left(x^2-1\right)}^5\right]$

Differentiate the following function w.r.t.$x$

$\log \sqrt{\frac{1-\cos {\displaystyle \frac{3x}{2}}}{1+\cos \frac{3x}{2}}}$

Differentiate the following function w.r.t.$x$

$\left(\log \sin x\right)\left(\log x\right)$

Differentiate the following function w.r.t $x$

$\log \left(\sec e^{x^2}\right)$

Differentiate the following function w.r.t $x$

$\log \left(x \tan x+\sec x\right)$

Differentiate the following functions w.r.t.$x$

$\frac{a^{\cos x}}{\sqrt{1+x^2}}$

Differentiate the following function w.r.t. $x$

$a^{5\sin x}$

Differentiate the following function w.r.t. $x$

$7^{x+\frac{1}{x}}$

Differentiate the following function w.r.t.$x$

$e^{x^2{\sin }^{2}x+{\cos }^{2}x}$

Differentiate the following function w.r.t.$x$

$e^{x+2\log x}$