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}

(x^{7} + y^{7}) d x + 7 x y^{6} d y = 0

x^{8 x}

\int_{- \infty}^{- 3} \frac{4}{x ^{5}} d x

\int + x^{9} x^{5} + 7 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}