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

The derivative of [tan(x^{2/3})]^3 is (2sec^2(x^{2/3})tan^2(x^{2/3}))/(x^{1/3)}

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

The first derivative of [tan(x^{2/3})]^3 is (2sec^2(x^{2/3})tan^2(x^{2/3}))/(x^{1/3)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

[tan (x^{\frac{2}{3}})]^{3}

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{x - 1}{( x - 1 ) ^{2} + 1} d x

f (t) = 7 + 10 x

\frac{d}{d x} (5 x ln (x))

\int \frac{1}{5 x - 3} d x

h \to 0 lim (\frac{( 2 ^{h} - 1 )}{h})

What is the derivative of [tan(x^{2/3})]^3 ?
The derivative of [tan(x^{2/3})]^3 is (2sec^2(x^{2/3})tan^2(x^{2/3}))/(x^{1/3)}
What is the first derivative of [tan(x^{2/3})]^3 ?
The first derivative of [tan(x^{2/3})]^3 is (2sec^2(x^{2/3})tan^2(x^{2/3}))/(x^{1/3)}