What is the derivative of (x^2/(x^2+16)) ?

The derivative of (x^2/(x^2+16)) is (32x)/((x^2+16)^2)

What is the first derivative of (x^2/(x^2+16)) ?

The first derivative of (x^2/(x^2+16)) is (32x)/((x^2+16)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (\frac{x ^{2}}{x ^{2} + 16})

\frac{32 x}{( x ^{2} + 16 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{x ^{2} + 16})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( x ^{2} + 16 ) - \frac{d}{d x} ( x ^{2} + 16 ) x ^{2}}{( x ^{2} + 16 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 16) = 2 x

= \frac{2 x ( x ^{2} + 16 ) - 2 x x ^{2}}{( x ^{2} + 16 ) ^{2}}

Simplify

\frac{2 x ( x ^{2} + 16 ) - 2 x x ^{2}}{( x ^{2} + 16 ) ^{2}} : \frac{32 x}{( x ^{2} + 16 ) ^{2}}

= \frac{32 x}{( x ^{2} + 16 ) ^{2}}

What is the derivative of (x^2/(x^2+16)) ?
The derivative of (x^2/(x^2+16)) is (32x)/((x^2+16)^2)
What is the first derivative of (x^2/(x^2+16)) ?
The first derivative of (x^2/(x^2+16)) is (32x)/((x^2+16)^2)