Exponential and Logarithmic Functions

If $y=a^{a^x}$ then $\frac{dy}{dx}=?$

Find the derivative of $\log x^2.$

If $y={\left(\frac{x}{n}\right)}^{nx}\left(1+\log \frac{x}{n}\right)$ then $y\text{'}\left(n\right)$ is given by

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 $y=2^x\log x,$ 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 $\frac{d}{dx}\left(e^{3x}\right)$

Derivative of $5^x$ w.r.t ${\log }_{5}x$ is

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

If $y=\log \left(\frac{x+\sqrt{x^2+a^2}}{\sqrt{x^2+a^2}-x}\right)$ then differentiate $y$ w.r.t $x$.

If $y=\ln x+e^x,$ then find $\frac{dy}{dx}.$

Differentiate $\frac{e^x+e^{-x}}{e^x-e^{-x}}$

Differentiate $\log \left(x+\sqrt{a^2+x^2}\right)$

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

Find the double differentiation of ${\tan }^{3}x·{\log }_{a}x$