What is the derivative of e^{0.5x^2} ?

The derivative of e^{0.5x^2} is e^{0.5x^2}x

What is the first derivative of e^{0.5x^2} ?

The first derivative of e^{0.5x^2} is e^{0.5x^2}x

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\frac{d}{d x} (e^{0.5 x^{2}})

e^{0.5 x^{2}} x

Solution steps

\frac{d}{d x} (e^{0.5 x^{2}})

Apply the chain rule:

e^{0.5 x^{2}} \frac{d}{d x} (0.5 x^{2})

= e^{0.5 x^{2}} \frac{d}{d x} (0.5 x^{2})

\frac{d}{d x} (0.5 x^{2}) = x

= e^{0.5 x^{2}} x

What is the derivative of e^{0.5x^2} ?
The derivative of e^{0.5x^2} is e^{0.5x^2}x
What is the first derivative of e^{0.5x^2} ?
The first derivative of e^{0.5x^2} is e^{0.5x^2}x