What is (\partial)/(\partial x)((63)/((9+x^2+y^2))) ?

The answer to (\partial)/(\partial x)((63)/((9+x^2+y^2))) is -(126x)/((9+x^2+y^2)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)((63)/((9+x^2+y^2)))

\frac{\partial}{\partial x} (\frac{63}{( 9 + x ^{2} + y ^{2} )})

- \frac{126 x}{( 9 + x ^{2} + y ^{2} ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{63}{( 9 + x ^{2} + y ^{2} )})

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 63 \frac{\partial}{\partial x} (\frac{1}{9 + x ^{2} + y ^{2}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 63 \frac{\partial}{\partial x} ((9 + x^{2} + y^{2})^{- 1})

Apply the chain rule:

- \frac{1}{( 9 + x ^{2} + y ^{2} ) ^{2}} \frac{\partial}{\partial x} (9 + x^{2} + y^{2})

= - \frac{1}{( 9 + x ^{2} + y ^{2} ) ^{2}} \frac{\partial}{\partial x} (9 + x^{2} + y^{2})

\frac{\partial}{\partial x} (9 + x^{2} + y^{2}) = 2 x

= 63 (- \frac{1}{( 9 + x ^{2} + y ^{2} ) ^{2}} \cdot 2 x)

Simplify

63 (- \frac{1}{( 9 + x ^{2} + y ^{2} ) ^{2}} \cdot 2 x) : - \frac{126 x}{( 9 + x ^{2} + y ^{2} ) ^{2}}

= - \frac{126 x}{( 9 + x ^{2} + y ^{2} ) ^{2}}

What is (\partial)/(\partial x)((63)/((9+x^2+y^2))) ?
The answer to (\partial)/(\partial x)((63)/((9+x^2+y^2))) is -(126x)/((9+x^2+y^2)^2)