Is differentiation of 2e^x^3 =
let y = 2e^x^3
let u = x^3
y = 2e^u
du/dx = 3x^2
dy/du = 2e^u
dy/dx = dy/du X du/dx
= 2e^u X 3x^2
= 2e^x^3 X 3x^2
= 6x^2.e^x^3
You have,
$\displaystyle e^{x^3}$
Let,
$\displaystyle u=x^3$
Then,
$\displaystyle y=e^u$
$\displaystyle u=x^3$
Thus,
$\displaystyle \frac{dy}{du}=e^u$
$\displaystyle \frac{du}{dx}=3x^2$
Then,
$\displaystyle \frac{dy}{dx}=\frac{dy}{du}\cdot \frac{du}{dx}$
Thus,
$\displaystyle \frac{dy}{dx}=3x^2e^u=3x^2e^{x^3}$
See the LaTeX tutorials at the beginning of this thread.
-Dan