What is the derivative of \sqrt[9]{3+tan(x}) ?

The derivative of \sqrt[9]{3+tan(x}) is (sec^2(x))/(9(3+tan(x))^{8/9)}

What is the first derivative of \sqrt[9]{3+tan(x}) ?

The first derivative of \sqrt[9]{3+tan(x}) is (sec^2(x))/(9(3+tan(x))^{8/9)}

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\frac{sec ^{2} ( x )}{9 ( 3 + tan ( x ) ) ^{\frac{8}{9}}}

Solution steps

Apply the chain rule:

\frac{1}{9 ( 3 + tan ( x ) ) ^{\frac{8}{9}}} \frac{d}{d x} (3 + tan (x))

= \frac{1}{9 ( 3 + tan ( x ) ) ^{\frac{8}{9}}} \frac{d}{d x} (3 + tan (x))

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

= \frac{1}{9 ( 3 + tan ( x ) ) ^{\frac{8}{9}}} sec^{2} (x)

Simplify

\frac{1}{9 ( 3 + tan ( x ) ) ^{\frac{8}{9}}} sec^{2} (x) : \frac{sec ^{2} ( x )}{9 ( 3 + tan ( x ) ) ^{\frac{8}{9}}}

= \frac{sec ^{2} ( x )}{9 ( 3 + tan ( x ) ) ^{\frac{8}{9}}}

What is the derivative of \sqrt[9]{3+tan(x}) ?
The derivative of \sqrt[9]{3+tan(x}) is (sec^2(x))/(9(3+tan(x))^{8/9)}
What is the first derivative of \sqrt[9]{3+tan(x}) ?
The first derivative of \sqrt[9]{3+tan(x}) is (sec^2(x))/(9(3+tan(x))^{8/9)}