What is the derivative of -e^(3x^2)?

Apr 19, 2018

$\frac{\mathrm{dy}}{\mathrm{dx}} = - 6 x {e}^{3 {x}^{2}}$

Explanation:

By using chain rule for the function of function concept

y=-e^(3x)^2)

$y = - {e}^{t}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = - {e}^{t} \frac{\mathrm{dt}}{\mathrm{dx}}$

$t = 3 {x}^{2}$

$t = 3 u$

$u = {x}^{2}$

$\frac{\mathrm{du}}{\mathrm{dx}} = 2 x$

(dt)/(dx)=3)du)/(dx)

3(du/(dx)=3xx2x

$\frac{\mathrm{dt}}{\mathrm{dx}} = 3 \times 2 x$

$3 \times 2 x = 6 x$

$\frac{\mathrm{dt}}{\mathrm{dx}} = 6 x$

$\frac{\mathrm{dy}}{\mathrm{dx}} = - {e}^{t} \frac{\mathrm{dt}}{\mathrm{dx}}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = - {e}^{3 {x}^{2}} \left(6 x\right)$

$\frac{\mathrm{dy}}{\mathrm{dx}} = - 6 x {e}^{3 {x}^{2}}$