1. ## Derivatives

Find derivative dy/dx if

a) y=tan^-1(1/2x)

b) y=4^(-x+3)

thanks!

2. Originally Posted by live_laugh_luv27
Find derivative dy/dx if

a) y=tan^-1(1/2x)

b) y=4^(-x+3)

thanks!
For the first function, just use the chain rule. Do you know how to show that $\frac{d}{dx}tan^{-1}(x)=\frac{1}{1+x^2}$ ?

The derivative of $y=tan^{-1}(\frac{1}{2x})$ is just $\frac{1}{1+(\frac{1}{2x})^2}(\frac{du}{dx})$ where $u=\frac{1}{2x}$

See if you can finish it.

3. $y=4^{-x+3}$

You can use the formula $\frac{d}{dx}(a^x)=a^xln(a)$ and the chain rule.