Exponential and Logarithmic Functions

If $y=a^{a^x}$ then $\frac{dy}{dx}=?$

Find the derivative of $\log x^2.$

Find $\frac{d}{dx}\left(e^x+x\log x\right)$

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

 $e^{{\sec }^{2}x}+3{\cos }^{-1}x$

The value of $\frac{d}{dx}\left(e^x\right),$ at $x=1$ is$?$

If $\frac{x^m}{y^n}={\left(xy\right)}^{\left(m-n\right)},\left(y\ne 0\right)$, find $\frac{dy}{dx}$.

If $x^y·y^x={\left(x+y\right)}^5$, find $\frac{dy}{dx}$.

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

Find the value of $\frac{d}{dx}\left(\sin x+{10}^x\right)$

If $x=\sqrt{a^{{\sin }^{-1}t}}, y=\sqrt{a^{{\cos }^{-1}t}},$$a>0$ and $-1<t<1,$ show that $\frac{dy}{dx}=-\frac{y}{x}$

Find the value of $\frac{d}{dx}\left(e^{3x}\right)$

Find $\frac{dy}{dx}$ for $y=\log \left(\frac{x+\sqrt{x^2+a^2}}{\sqrt{x^2+a^2}-x}\right)$

If $y=6^{e^x.\sin x}, \text{then find the value of }\frac{dy}{dx}.$

If $\log \left(\frac{a+b}{3}\right)=\frac{\log a+\log b}{2}$, then find the value of $\frac{a}{b}+\frac{b}{a}.$

Evaluate $\int 2^{2^{2^x}}{2}^{2^x}{2}^{x}dx$

What is logarithm?

Is it true that $x=e^{\log x}$ for all real $x$?

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

$4^{{\log }_{2}secx}-9^{{\log }_3\tan x}$

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

$\log \left[a^{4x}{\left(\frac{x-5}{x+4}\right)}^{\frac{3}{4}}\right]$

If $y=\sin \left(x^x\right)$, find $\frac{dy}{dx}$