What is the derivative of \sqrt[3]{3+tan(t)} ?

The derivative of \sqrt[3]{3+tan(t)} is (sec^2(t))/(3(3+tan(t))^{2/3)}

What is the first derivative of \sqrt[3]{3+tan(t)} ?

The first derivative of \sqrt[3]{3+tan(t)} is (sec^2(t))/(3(3+tan(t))^{2/3)}

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derivative of

\frac{sec ^{2} ( t )}{3 ( 3 + tan ( t ) ) ^{\frac{2}{3}}}

Solution steps

Apply the chain rule:

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

= \frac{1}{3 ( 3 + tan ( t ) ) ^{\frac{2}{3}}} \frac{d}{d t} (3 + tan (t))

\frac{d}{d t} (3 + tan (t)) = sec^{2} (t)

= \frac{1}{3 ( 3 + tan ( t ) ) ^{\frac{2}{3}}} sec^{2} (t)

Simplify

\frac{1}{3 ( 3 + tan ( t ) ) ^{\frac{2}{3}}} sec^{2} (t) : \frac{sec ^{2} ( t )}{3 ( 3 + tan ( t ) ) ^{\frac{2}{3}}}

= \frac{sec ^{2} ( t )}{3 ( 3 + tan ( t ) ) ^{\frac{2}{3}}}

What is the derivative of \sqrt[3]{3+tan(t)} ?
The derivative of \sqrt[3]{3+tan(t)} is (sec^2(t))/(3(3+tan(t))^{2/3)}
What is the first derivative of \sqrt[3]{3+tan(t)} ?
The first derivative of \sqrt[3]{3+tan(t)} is (sec^2(t))/(3(3+tan(t))^{2/3)}