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

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

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(\partial)/(\partial x)(1/((x+y)))

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

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

Solution steps

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

Treat

y

as a constant

Apply exponent rule:

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

= \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

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

Simplify

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

\int 4 t^{4} e^{6 t^{5}} d t

n \to \infty lim ((1)^{n})

\frac{d y}{d x} (x + y) = x - y

\frac{d}{d t} (- e^{2 t})

x \to 0 lim (\frac{cos ( 2 x ) - cos ( 5 x )}{x ^{2}})

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