What is the derivative of \sqrt[3]{2+tan(x}) ?

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

What is the first derivative of \sqrt[3]{2+tan(x}) ?

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

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

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int t^{2} sin (2 t) d t

f (x) = x^{\frac{1}{4}}

x \to + \frac{π}{2} lim (tan (x))

2 + 3 x

y^{^{'}} - 2 y = t^{2} e^{2 t}

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