What is the derivative of 1/3 tan^3(1/x) ?

The derivative of 1/3 tan^3(1/x) is -(sec^2(1/x)tan^2(1/x))/(x^2)

What is the first derivative of 1/3 tan^3(1/x) ?

The first derivative of 1/3 tan^3(1/x) is -(sec^2(1/x)tan^2(1/x))/(x^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

(x^{2} - x) y^{^{'}} = y - 2 x y

cos^{4} (θ + 5)

n = 1 \sum \infty \frac{n}{n ^{3} + 1}

\frac{2}{3 x + 1}

(2 x + 3)^{5} + 10 x (2 x + 3)^{4}

What is the derivative of 1/3 tan^3(1/x) ?
The derivative of 1/3 tan^3(1/x) is -(sec^2(1/x)tan^2(1/x))/(x^2)
What is the first derivative of 1/3 tan^3(1/x) ?
The first derivative of 1/3 tan^3(1/x) is -(sec^2(1/x)tan^2(1/x))/(x^2)