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 $\displaystyle \frac{d}{dx}tan^{-1}(x)=\frac{1}{1+x^2}$ ?
The derivative of $\displaystyle y=tan^{-1}(\frac{1}{2x})$ is just $\displaystyle \frac{1}{1+(\frac{1}{2x})^2}(\frac{du}{dx})$ where $\displaystyle u=\frac{1}{2x}$
See if you can finish it.