Solve $\frac{d}{d x} e^{3 x^{2}}$

Step-by-step solution

Step 1 · Identify the inner function
$u = 3 x^{2}, u^{'} = 6 x$
The exponential contains a function of x, so the chain rule is required.
Step 2 · Chain rule
$\frac{d}{d x} e^{u} = e^{u} u^{'} = 6 x e^{3 x^{2}}$
Differentiate the exponential, then multiply by the derivative of its exponent. Valid for all real x.

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