What is the derivative of ae^{ax} ?

The derivative of ae^{ax} is a^2e^{ax}

What is the first derivative of ae^{ax} ?

The first derivative of ae^{ax} is a^2e^{ax}

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

a^{2} e^{a x}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (a x) = a

= a e^{a x} a

Simplify

a e^{a x} a : a^{2} e^{a x}

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

What is the derivative of ae^{ax} ?
The derivative of ae^{ax} is a^2e^{ax}
What is the first derivative of ae^{ax} ?
The first derivative of ae^{ax} is a^2e^{ax}