Question

How do you determine the derivative of this exponential function `f(x) = sqrt (3^x) / x^2`?

Answer 1

Write the function as `f(x)=\frac{3^{x/2}}{x^2}` and then use the Quotient Rule and the Chain Rule:

`f'(x)=\frac{x^{2}\cdot ln(3)\cdot 3^{x/2}\cdot \frac{1}{2}-3^{x/2}\cdot 2x}{x^{4}}=\frac{3^{x/2}\cdot(ln(\sqrt{3})\cdot x-2)}{x^{3}}`