Question

Find the differentiation of a function represented by $y=e^{x^3}$ with respect to $x$.

• A. $e^{x^3}.3x^3$
• B. $e^{x^2}.3x^2$
• C. $e^{x^3}\times 3x^2$
• D. $e^{x^3}.3x$

Answer 1

The correct option is C $e^{x^3}\times 3x^2$

$y=e^{x^3}$ (Given)
Let $u=x^3$ so that $y=e^u$

Differentiating $y$ with respect to the $x$, using chain rule gives:

$\frac{dy}{dx}=\frac{dy}{du}\times \frac{du}{dx}$

$\because \frac{dy}{du}=e^u$ and $\frac{du}{dx}=3x^2$

$\therefore \frac{dy}{dx}=e^u\times 3x^2$
Substituting $u=x^3$

$\Rightarrow \frac{dy}{dx}=e^{x^3}\times 3x^2$