What is the derivative of 3e^{2x^2} ?

The derivative of 3e^{2x^2} is 12e^{2x^2}x

What is the first derivative of 3e^{2x^2} ?

The first derivative of 3e^{2x^2} is 12e^{2x^2}x

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derivative of

3 e^{2 x^{2}}

12 e^{2 x^{2}} x

Solution steps

\frac{d}{d x} (3 e^{2 x^{2}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (e^{2 x^{2}})

Apply the chain rule:

e^{2 x^{2}} \frac{d}{d x} (2 x^{2})

= e^{2 x^{2}} \frac{d}{d x} (2 x^{2})

\frac{d}{d x} (2 x^{2}) = 4 x

= 3 e^{2 x^{2}} \cdot 4 x

Simplify

= 12 e^{2 x^{2}} x

What is the derivative of 3e^{2x^2} ?
The derivative of 3e^{2x^2} is 12e^{2x^2}x
What is the first derivative of 3e^{2x^2} ?
The first derivative of 3e^{2x^2} is 12e^{2x^2}x