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} (sin (- 6 x))

\int (2 x - 5) e^{x} d x

x \to 0 + lim (2 x^{x})

\int (ln (x + 1 + x^{2})) d x

\frac{\partial}{\partial x} (x \cdot e^{y})

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}