Question

What is the derivative of `f(x)=b^x` ?

Answer 1

This is the exponential function of base `b` (where `b>0` should be assumed). It can be thought of as `b^x=e^(xln(b))`, so that, using the Chain Rule (See Chain Rule ) and the fact that `(e^x)'=e^x` (see Exponentials with Base e ) yields `(b^x)'=e^(xln(b))\times ln(b)=b^x\times ln(b)`
(see Exponential functions ).