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}

\frac{d}{d x} ((x^{3} + 2 x - 7) (3 + x - x^{2}))

\frac{d}{d x} ((x + \frac{1}{x})^{- 1})

\frac{d y}{d x} - 2 x y = 8 x

x \to 1 - lim (∣ x - 1 ∣)

\int \frac{4 x ^{3}}{e ^{2 x^{2}}} d 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}