What is (\partial)/(\partial x)(x/(x^2+81)) ?

The answer to (\partial)/(\partial x)(x/(x^2+81)) is (-x^2+81)/((x^2+81)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(x/(x^2+81))

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + 81})

\frac{- x ^{2} + 81}{( x ^{2} + 81 ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + 81})

Apply the Quotient Rule:

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

= \frac{\frac{\partial}{\partial x} ( x ) ( x ^{2} + 81 ) - \frac{\partial}{\partial x} ( x ^{2} + 81 ) x}{( x ^{2} + 81 ) ^{2}}

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (x^{2} + 81) = 2 x

= \frac{1 \cdot ( x ^{2} + 81 ) - 2 xx}{( x ^{2} + 81 ) ^{2}}

1 \cdot (x^{2} + 81) - 2 xx = - x^{2} + 81

= \frac{- x ^{2} + 81}{( x ^{2} + 81 ) ^{2}}

What is (\partial)/(\partial x)(x/(x^2+81)) ?
The answer to (\partial)/(\partial x)(x/(x^2+81)) is (-x^2+81)/((x^2+81)^2)