What is the derivative of ae^{-3x} ?

The derivative of ae^{-3x} is -3ae^{-3x}

What is the first derivative of ae^{-3x} ?

The first derivative of ae^{-3x} is -3ae^{-3x}

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\frac{d}{d x} (a e^{- 3 x})

- 3 a e^{- 3 x}

Solution steps

\frac{d}{d x} (a e^{- 3 x})

Take the constant out:

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

= a \frac{d}{d x} (e^{- 3 x})

Apply the chain rule:

e^{- 3 x} \frac{d}{d x} (- 3 x)

= e^{- 3 x} \frac{d}{d x} (- 3 x)

\frac{d}{d x} (- 3 x) = - 3

= a e^{- 3 x} (- 3)

Simplify

= - 3 a e^{- 3 x}

\frac{\partial}{\partial x} (x + 1)

\frac{\partial}{\partial x} (z^{4} x^{0.5})

\frac{d y}{d x} = (2 x + 1) (y + 1), y (- 1) = 1

\frac{d y}{d x} = y (5 x^{2} + 3)

\int_{1}^{4} \frac{4}{x ^{2}} d x

What is the derivative of ae^{-3x} ?
The derivative of ae^{-3x} is -3ae^{-3x}
What is the first derivative of ae^{-3x} ?
The first derivative of ae^{-3x} is -3ae^{-3x}