Question

given: f(x) = exp(xlna) find f'(x)

Answer 1

f(x)=a^x

Answer 2

If you are looking for the derivative remember that xln(a) equals ln(a^x) because log rules allow you to move the power in front of log. So we know that e^x derivative is e^x so e^xlna equals the derivative of e^lna^x which is e^ln(a^x) * ln(a) since the ln(a) is the coeffecient of x which you must take the derivative of by the chain rule. So f'(x)=e^(ln(a^x))*ln(a) but we also know that e^ln(a^x) equals a^x since e^ln equals 1. So f'(x) = (a^x)ln(a)