How do you find the derivative of 3^(x^2-2)?

Jun 22, 2016

$\ln 9 \setminus x \setminus {3}^{{x}^{2} - 2}$

Explanation:

let $y = {3}^{{x}^{2} - 2}$

so $\ln y = \ln \left({3}^{{x}^{2} - 2}\right) = \left({x}^{2} - 2\right) \ln 3$

$\setminus \implies \frac{1}{y} y ' = 2 x \ln 3$

$y ' = 2 x \ln 3 \cdot y = 2 \setminus \ln 3 \setminus x \setminus {3}^{{x}^{2} - 2}$

$= \ln 9 \setminus x \setminus {3}^{{x}^{2} - 2}$