What is the derivative of e^{-bx} ?

The derivative of e^{-bx} is -be^{-bx}

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

The first derivative of e^{-bx} is -be^{-bx}

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

- b e^{- b x}

Solution steps

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

Apply the chain rule:

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

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

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

= e^{- b x} (- b)

Simplify

= - b e^{- b x}

\int 64 e^{4 x} sin (4 x) d x

\int (e^{y})^{2} d y

x \to 0 + lim (\frac{1}{x ln ( x )})

\int \frac{1}{x ^{6}} + \frac{3}{x ^{2}} d x

2 x e^{x} + e^{x} x^{2}

What is the derivative of e^{-bx} ?
The derivative of e^{-bx} is -be^{-bx}
What is the first derivative of e^{-bx} ?
The first derivative of e^{-bx} is -be^{-bx}