What is (\partial)/(\partial x)(-1/((10+x*y))) ?

The answer to (\partial)/(\partial x)(-1/((10+x*y))) is y/((10+xy)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(-1/((10+x*y)))

\frac{\partial}{\partial x} (- \frac{1}{( 10 + x \cdot y )})

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

Solution steps

\frac{\partial}{\partial x} (- \frac{1}{( 10 + x y )})

Treat

y

as a constant

Take the constant out:

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

= - \frac{\partial}{\partial x} (\frac{1}{10 + x y})

Apply exponent rule:

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

= - \frac{\partial}{\partial x} ((10 + x y)^{- 1})

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (10 + x y) = y

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

Simplify

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

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

What is (\partial)/(\partial x)(-1/((10+x*y))) ?
The answer to (\partial)/(\partial x)(-1/((10+x*y))) is y/((10+xy)^2)