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

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

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

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

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

- 3 e^{- 3 x}

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \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

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

Simplify

= - 3 e^{- 3 x}

\int \frac{u}{u ^{2} + 4} d u

y = 6 x

y = cos (tan (x))

\int_{0}^{π} 3 sin^{3} (x) d x

\frac{d}{d x} ((ln (x))^{2} cos (x))

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