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Popular >

derivative of \sqrt[3]{tan(5x})

Solution

Solution

\frac{5 sec ^{2} ( 5 x )}{3 tan ^{\frac{2}{3}} ( 5 x )}

Solution steps

Apply the chain rule:

\frac{1}{3 ( tan ( 5 x ) ) ^{\frac{2}{3}}} \frac{d}{d x} (tan (5 x))

= \frac{1}{3 ( tan ( 5 x ) ) ^{\frac{2}{3}}} \frac{d}{d x} (tan (5 x))

\frac{d}{d x} (tan (5 x)) = sec^{2} (5 x) \cdot 5

= \frac{1}{3 ( tan ( 5 x ) ) ^{\frac{2}{3}}} sec^{2} (5 x) \cdot 5

Simplify

\frac{1}{3 tan ^{\frac{2}{3}} ( 5 x )} sec^{2} (5 x) \cdot 5 : \frac{5 sec ^{2} ( 5 x )}{3 tan ^{\frac{2}{3}} ( 5 x )}

= \frac{5 sec ^{2} ( 5 x )}{3 tan ^{\frac{2}{3}} ( 5 x )}

Popular Examples

integral of (27)/(1-cos(9x))

\int \frac{27}{1 - cos ( 9 x )} d x

(dy)/(dx)=(2+y^2)/(2xy)

\frac{d y}{d x} = \frac{2 + y ^{2}}{2 x y}

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\int_{1}^{6} 12 x^{3} - 9 x^{2} + 2 d x

derivative of log_{2}(((3x+1)/(x^2+1)))

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

derivative of (7x/((x^2+1)^{3/5)})

\frac{d}{d x} (\frac{7 x}{( x ^{2} + 1 ) ^{\frac{3}{5}}})

Frequently Asked Questions (FAQ)

What is the derivative of \sqrt[3]{tan(5x}) ?
The derivative of \sqrt[3]{tan(5x}) is (5sec^2(5x))/(3tan^{2/3)(5x)}
What is the first derivative of \sqrt[3]{tan(5x}) ?
The first derivative of \sqrt[3]{tan(5x}) is (5sec^2(5x))/(3tan^{2/3)(5x)}