What is the derivative of 1/4 e^{2x^2} ?

The derivative of 1/4 e^{2x^2} is e^{2x^2}x

What is the first derivative of 1/4 e^{2x^2} ?

The first derivative of 1/4 e^{2x^2} is e^{2x^2}x

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\frac{d}{d x} (\frac{1}{4} e^{2 x^{2}})

e^{2 x^{2}} x

Solution steps

\frac{d}{d x} (\frac{1}{4} e^{2 x^{2}})

Take the constant out:

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

= \frac{1}{4} \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

= \frac{1}{4} e^{2 x^{2}} \cdot 4 x

Simplify

\frac{1}{4} e^{2 x^{2}} \cdot 4 x : e^{2 x^{2}} x

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

What is the derivative of 1/4 e^{2x^2} ?
The derivative of 1/4 e^{2x^2} is e^{2x^2}x
What is the first derivative of 1/4 e^{2x^2} ?
The first derivative of 1/4 e^{2x^2} is e^{2x^2}x