What is the derivative of (2tan(x)/x) ?

The derivative of (2tan(x)/x) is (2(xsec^2(x)-tan(x)))/(x^2)

What is the first derivative of (2tan(x)/x) ?

The first derivative of (2tan(x)/x) is (2(xsec^2(x)-tan(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{2 tan ( x )}{x})

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d x}{d x} = 1

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

Simplify

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

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

n = 0 \sum \infty \frac{1}{5 n + 1}

2 x^{3} - 4 x + 6

\frac{\partial}{\partial x} (5 - 3 x + 6 y - 2 x^{2} y)

(1, 6), (7, 3)

\int x^{3} y d y

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