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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 tan (x^{2})) = 6 x sec^{2} (x^{2})

= \frac{1}{3 ( 3 tan ( x ^{2} ) ) ^{\frac{2}{3}}} \cdot 6 x sec^{2} (x^{2})

Simplify

\frac{1}{3 ( 3 tan ( x ^{2} ) ) ^{\frac{2}{3}}} \cdot 6 x sec^{2} (x^{2}) : \frac{2 x sec ^{2} ( x ^{2} )}{3 ^{\frac{2}{3}} tan ^{\frac{2}{3}} ( x ^{2} )}

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

\int 4 - 2 x d x

\int \frac{x ^{2}}{2} + x d x

\frac{\partial}{\partial x} (x \cdot sin (x y))

\int 5 x^{\frac{1}{3}} + 4 x^{- \frac{1}{3}} + 11 d x

\frac{d}{d x} (\frac{( x ) ^{3}}{( 2 x ^{7} + x ) ^{2}})

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