What is (\partial)/(\partial x)((-4)/(x+y)) ?

The answer to (\partial)/(\partial x)((-4)/(x+y)) is 4/((x+y)^2)

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(\partial)/(\partial x)((-4)/(x+y))

\frac{\partial}{\partial x} (\frac{- 4}{x + y})

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

Solution steps

\frac{\partial}{\partial x} (\frac{- 4}{x + y})

Simplify

\frac{- 4}{x + y} : - \frac{4}{x + y}

= \frac{\partial}{\partial x} (- \frac{4}{x + y})

Treat

y

as a constant

Take the constant out:

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

= - 4 \frac{\partial}{\partial x} (\frac{1}{x + y})

Apply exponent rule:

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

= - 4 \frac{\partial}{\partial x} ((x + y)^{- 1})

Apply the chain rule:

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

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

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

= - 4 (- \frac{1}{( x + y ) ^{2}} \cdot 1)

Simplify

- 4 (- \frac{1}{( x + y ) ^{2}} \cdot 1) : \frac{4}{( x + y ) ^{2}}

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

y = \frac{1}{7 x ^{\frac{6}{7}}}

x \to 0 lim (\frac{6 x}{sin ( x )})

f (x) = x^{2} - 7, (4, 9)

\frac{( s + 1 )}{( s ^{2} + 4 s + 20 )}

x \to - \infty lim (\frac{4 + 5 e ^{4 x}}{5 - 6 e ^{5 x}})

What is (\partial)/(\partial x)((-4)/(x+y)) ?
The answer to (\partial)/(\partial x)((-4)/(x+y)) is 4/((x+y)^2)