What is the derivative of ae^{-2x} ?

The derivative of ae^{-2x} is -2ae^{-2x}

What is the first derivative of ae^{-2x} ?

The first derivative of ae^{-2x} is -2ae^{-2x}

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\frac{d}{d x} (a e^{- 2 x})

- 2 a e^{- 2 x}

Solution steps

\frac{d}{d x} (a e^{- 2 x})

Take the constant out:

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

= a \frac{d}{d x} (e^{- 2 x})

Apply the chain rule:

e^{- 2 x} \frac{d}{d x} (- 2 x)

= e^{- 2 x} \frac{d}{d x} (- 2 x)

\frac{d}{d x} (- 2 x) = - 2

= a e^{- 2 x} (- 2)

Simplify

= - 2 a e^{- 2 x}

\frac{d y}{d x}, 4 x^{2} y^{7} - 2 x = x^{5} + 4 y^{3}

\frac{d}{d x} (4 x (x^{2} - 2)^{2})

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

f (x) = x^{3} - 4

\int (1 - x - y)^{2} d y

What is the derivative of ae^{-2x} ?
The derivative of ae^{-2x} is -2ae^{-2x}
What is the first derivative of ae^{-2x} ?
The first derivative of ae^{-2x} is -2ae^{-2x}