What is the derivative of-ae^{-x} ?

The derivative of-ae^{-x} is ae^{-x}

What is the first derivative of-ae^{-x} ?

The first derivative of-ae^{-x} is ae^{-x}

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

a e^{- x}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= - a e^{- x} (- 1)

Simplify

= a e^{- x}

\frac{\partial ^{2}}{\partial y ^{2}} (x^{2} - e^{y^{2}})

\int_{0}^{\frac{π}{8}} x tan^{2} (2 x) d x

\int \frac{1}{4 u ^{2} + 9 - 41 u} d u

- sin (2 t)

\int \frac{1}{5 + 4 cos ( x )} d x

What is the derivative of-ae^{-x} ?
The derivative of-ae^{-x} is ae^{-x}
What is the first derivative of-ae^{-x} ?
The first derivative of-ae^{-x} is ae^{-x}