What is the derivative of 15e^{x^2} ?

The derivative of 15e^{x^2} is 30e^{x^2}x

What is the first derivative of 15e^{x^2} ?

The first derivative of 15e^{x^2} is 30e^{x^2}x

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derivative of

15 e^{x^{2}}

30 e^{x^{2}} x

Solution steps

\frac{d}{d x} (15 e^{x^{2}})

Take the constant out:

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

= 15 \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

= 15 e^{x^{2}} \cdot 2 x

Simplify

= 30 e^{x^{2}} x

What is the derivative of 15e^{x^2} ?
The derivative of 15e^{x^2} is 30e^{x^2}x
What is the first derivative of 15e^{x^2} ?
The first derivative of 15e^{x^2} is 30e^{x^2}x