What is the derivative of (x^2+3/(x^2+5)) ?

The derivative of (x^2+3/(x^2+5)) is (4x)/((x^2+5)^2)

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

The first derivative of (x^2+3/(x^2+5)) is (4x)/((x^2+5)^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{x ^{2} + 3}{x ^{2} + 5})

\frac{4 x}{( x ^{2} + 5 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

2 x (x^{2} + 5) - 2 x (x^{2} + 3) : 4 x

= \frac{4 x}{( x ^{2} + 5 ) ^{2}}

\int cos^{3} (x s i) n^{2} x d x

\frac{\partial}{\partial x} (- 3 \cdot x^{2} + 28)

\int 2 e^{\frac{x}{2}} x^{3} d x

\frac{\partial}{\partial x} (e^{- r (x - c t)^{2}})

\frac{d}{d x} (\frac{3 - 5 x - x ^{2}}{x ^{2} - 6})

What is the derivative of (x^2+3/(x^2+5)) ?
The derivative of (x^2+3/(x^2+5)) is (4x)/((x^2+5)^2)
What is the first derivative of (x^2+3/(x^2+5)) ?
The first derivative of (x^2+3/(x^2+5)) is (4x)/((x^2+5)^2)