What is the derivative of f(x)= 1/((e^x)^3) ?

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

What is the first derivative of f(x)= 1/((e^x)^3) ?

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

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derivative of

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

- \frac{3}{e ^{3 x}}

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{3}{( e ^{x} ) ^{4}} \frac{d}{d x} (e^{x})

= - \frac{3}{( e ^{x} ) ^{4}} \frac{d}{d x} (e^{x})

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

= - \frac{3}{( e ^{x} ) ^{4}} e^{x}

Simplify

- \frac{3}{( e ^{x} ) ^{4}} e^{x} : - \frac{3}{e ^{3 x}}

= - \frac{3}{e ^{3 x}}

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x \to 0 lim (e^{- 3 x})

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