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

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

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

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

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derivative of

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

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{x ^{3}}{x ^{2} - 9} d x

\frac{\partial}{\partial y} (6 + x ln (x y - 7))

\frac{\partial}{\partial x} (x y (1 - x - y))

\frac{d}{d x} (\frac{2}{sin ( x )})

sin (2 x), 0

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