What is the derivative of 1-e^{-ax} ?

The derivative of 1-e^{-ax} is ae^{-ax}

What is the first derivative of 1-e^{-ax} ?

The first derivative of 1-e^{-ax} is ae^{-ax}

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\frac{d}{d x} (1 - e^{- a x})

a e^{- a x}

Solution steps

\frac{d}{d x} (1 - e^{- a x})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (1) - \frac{d}{d x} (e^{- a x})

\frac{d}{d x} (1) = 0

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

= 0 - (- a e^{- a x})

Simplify

= a e^{- a x}

\int_{- 1}^{2} y^{3} + 8 d y

\int (1 - t) e^{12 t - 6 t^{2}} d t

y^{^{'}} = y (x y^{2} + 2)

\int x (x + 1) d x

\frac{d}{d x} (\frac{x ^{2}}{1 + x ^{3}})

What is the derivative of 1-e^{-ax} ?
The derivative of 1-e^{-ax} is ae^{-ax}
What is the first derivative of 1-e^{-ax} ?
The first derivative of 1-e^{-ax} is ae^{-ax}