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

The derivative of (2x^2-3/(x^2+1)) is (10x)/((x^2+1)^2)

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

The first derivative of (2x^2-3/(x^2+1)) is (10x)/((x^2+1)^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 x ^{2} - 3}{x ^{2} + 1})

\frac{10 x}{( x ^{2} + 1 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (2 x^{2} - 3) = 4 x

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

= \frac{4 x ( x ^{2} + 1 ) - 2 x ( 2 x ^{2} - 3 )}{( x ^{2} + 1 ) ^{2}}

Expand

4 x (x^{2} + 1) - 2 x (2 x^{2} - 3) : 10 x

= \frac{10 x}{( x ^{2} + 1 ) ^{2}}

(5 x^{2})^{^{'}}

y^{^{'}} + 2 t y = 5 t

y = x^{2}, y = 18 - x^{2}

y = x^{2}, x = 3

(x, y) \to (0, 0) lim (\frac{x ^{2} + y ^{2}}{9 + y ^{2}})

What is the derivative of (2x^2-3/(x^2+1)) ?
The derivative of (2x^2-3/(x^2+1)) is (10x)/((x^2+1)^2)
What is the first derivative of (2x^2-3/(x^2+1)) ?
The first derivative of (2x^2-3/(x^2+1)) is (10x)/((x^2+1)^2)