What is the derivative of y= 1/(\sqrt[3]{e^x)} ?

The derivative of y= 1/(\sqrt[3]{e^x)} is -1/(3e^{x/3)}

What is the first derivative of y= 1/(\sqrt[3]{e^x)} ?

The first derivative of y= 1/(\sqrt[3]{e^x)} is -1/(3e^{x/3)}

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derivative of

- \frac{1}{3 e ^{\frac{x}{3}}}

Solution steps

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{1}{3 ( e ^{x} ) ^{\frac{4}{3}}} \frac{d}{d x} (e^{x})

= - \frac{1}{3 ( e ^{x} ) ^{\frac{4}{3}}} \frac{d}{d x} (e^{x})

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

= - \frac{1}{3 ( e ^{x} ) ^{\frac{4}{3}}} e^{x}

Simplify

- \frac{1}{3 ( e ^{x} ) ^{\frac{4}{3}}} e^{x} : - \frac{1}{3 e ^{\frac{x}{3}}}

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

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What is the derivative of y= 1/(\sqrt[3]{e^x)} ?
The derivative of y= 1/(\sqrt[3]{e^x)} is -1/(3e^{x/3)}
What is the first derivative of y= 1/(\sqrt[3]{e^x)} ?
The first derivative of y= 1/(\sqrt[3]{e^x)} is -1/(3e^{x/3)}