What is the derivative of ((x+5/(x^2+2))^2) ?

The derivative of ((x+5/(x^2+2))^2) is (2(x+5)(-x^2-10x+2))/((x^2+2)^3)

What is the first derivative of ((x+5/(x^2+2))^2) ?

The first derivative of ((x+5/(x^2+2))^2) is (2(x+5)(-x^2-10x+2))/((x^2+2)^3)

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{x + 5}{x ^{2} + 2})^{2})

\frac{2 ( x + 5 ) ( - x ^{2} - 10 x + 2 )}{( x ^{2} + 2 ) ^{3}}

Solution steps

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

Apply the chain rule:

2 \cdot \frac{x + 5}{x ^{2} + 2} \frac{d}{d x} (\frac{x + 5}{x ^{2} + 2})

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

\frac{d}{d x} (\frac{x + 5}{x ^{2} + 2}) = \frac{- x ^{2} - 10 x + 2}{( x ^{2} + 2 ) ^{2}}

= 2 \cdot \frac{x + 5}{x ^{2} + 2} \cdot \frac{- x ^{2} - 10 x + 2}{( x ^{2} + 2 ) ^{2}}

Simplify

2 \cdot \frac{x + 5}{x ^{2} + 2} \cdot \frac{- x ^{2} - 10 x + 2}{( x ^{2} + 2 ) ^{2}} : \frac{2 ( x + 5 ) ( - x ^{2} - 10 x + 2 )}{( x ^{2} + 2 ) ^{3}}

= \frac{2 ( x + 5 ) ( - x ^{2} - 10 x + 2 )}{( x ^{2} + 2 ) ^{3}}

x \to 1 + lim (x - 1)

x \to 0 + lim (e^{\frac{1}{x} l n (x)})

\int_{0}^{1} \frac{7 y}{e ^{2 y}} d y

- 2 y^{^{'}} + \frac{2 y}{x} = x^{4} y^{3}

n = 1 \sum \infty \frac{( n ^{n} )}{n !}

What is the derivative of ((x+5/(x^2+2))^2) ?
The derivative of ((x+5/(x^2+2))^2) is (2(x+5)(-x^2-10x+2))/((x^2+2)^3)
What is the first derivative of ((x+5/(x^2+2))^2) ?
The first derivative of ((x+5/(x^2+2))^2) is (2(x+5)(-x^2-10x+2))/((x^2+2)^3)