What is the derivative of ((x^2-1/(x^2+1))^2) ?

The derivative of ((x^2-1/(x^2+1))^2) is (8x(x^2-1))/((x^2+1)^3)

What is the first derivative of ((x^2-1/(x^2+1))^2) ?

The first derivative of ((x^2-1/(x^2+1))^2) is (8x(x^2-1))/((x^2+1)^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 ^{2} - 1}{x ^{2} + 1})^{2})

\frac{8 x ( x ^{2} - 1 )}{( x ^{2} + 1 ) ^{3}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x ^{2} - 1}{x ^{2} + 1}) = \frac{4 x}{( x ^{2} + 1 ) ^{2}}

= 2 \cdot \frac{x ^{2} - 1}{x ^{2} + 1} \cdot \frac{4 x}{( x ^{2} + 1 ) ^{2}}

Simplify

2 \cdot \frac{x ^{2} - 1}{x ^{2} + 1} \cdot \frac{4 x}{( x ^{2} + 1 ) ^{2}} : \frac{8 x ( x ^{2} - 1 )}{( x ^{2} + 1 ) ^{3}}

= \frac{8 x ( x ^{2} - 1 )}{( x ^{2} + 1 ) ^{3}}

\frac{d}{d x} (x^{\frac{y}{z}})

f (x) = (3 x - 1) (5 x + 2)

\int 7 x e^{- x (y + 7)} d x

f (x) = ln (x x^{2} + 1)

f (x) = 3 x - 6 x

What is the derivative of ((x^2-1/(x^2+1))^2) ?
The derivative of ((x^2-1/(x^2+1))^2) is (8x(x^2-1))/((x^2+1)^3)
What is the first derivative of ((x^2-1/(x^2+1))^2) ?
The first derivative of ((x^2-1/(x^2+1))^2) is (8x(x^2-1))/((x^2+1)^3)