Browse Questions

# Differentiate the following w.r.t. $x : e^{x^{3} }$

$\begin{array}{1 1} 3x^2\;e^{x^3} \\3x\;e^{x^3} \\ 3x^{-2}\;e^{x^2} \\ 3x^2\;e^{x^2} \end{array}$

Toolbox:
• According to the Chain Rule for differentiation, given two functions $f(x)$ and $g(x)$, and $y=f(g(x)) \rightarrow y' = f'(g(x)).g'(x)$.
• $\; \large \frac{d(e^x)}{dx} $$= e^x Given y = e^{x^3} This is of the form y = f(g(x)), where g(x) = x^3. We can solve this using the chain rule of differentiation. According to the Chain Rule for differentiation, given two functions f(x) and g(x), and y=f(g(x)) \rightarrow y' = f'(g(x)).g'(x). If g(x) = x^3, then g'(x) = 3\;x^2 \; \large \frac{d(e^x)}{dx}$$= e^x$
$\Rightarrow y' = e^{x^3}\; 3\;x^2 = 3x^2\;e^{x^3}$