What is the derivative of 1/3 e^{-3x} ?

The derivative of 1/3 e^{-3x} is -e^{-3x}

What is the first derivative of 1/3 e^{-3x} ?

The first derivative of 1/3 e^{-3x} is -e^{-3x}

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\frac{d}{d x} (\frac{1}{3} e^{- 3 x})

- e^{- 3 x}

Solution steps

\frac{d}{d x} (\frac{1}{3} e^{- 3 x})

Take the constant out:

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

= \frac{1}{3} \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

= \frac{1}{3} e^{- 3 x} (- 3)

Simplify

\frac{1}{3} e^{- 3 x} (- 3) : - e^{- 3 x}

= - e^{- 3 x}

\frac{1}{( s ^{2} + 2 s + 2 ) ( s ^{2} + 9 )}

\frac{d}{d x} ((3 x + 1)^{2})

\int \frac{200}{16 x ^{2} + 256} d x

\frac{d ^{2} y}{d x ^{2}} = 4 y, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} - y^{^{'}} = x e^{x}

What is the derivative of 1/3 e^{-3x} ?
The derivative of 1/3 e^{-3x} is -e^{-3x}
What is the first derivative of 1/3 e^{-3x} ?
The first derivative of 1/3 e^{-3x} is -e^{-3x}