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

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

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

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

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

e^{x^{2}} x

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= e^{x^{2}} x

\frac{x ^{2}}{5 ( 1 - x )}

f (x) = 2 x^{2} + x - 1, at a = - 1

\int 9 sin (3 x) d x

x \to - 2 lim (x^{2} - 4)

f (x) = x^{\frac{4}{3}}

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