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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial x} (y) = 0

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

= 0 - \frac{1}{( x + y ) ^{2}}

Simplify

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

\frac{d}{d x} (lo g_{3} (sec (2 x)))

x \to 0 lim (tan (x) - sec (x))

(t e)^{3} e^{- 2 t} e^{- 2}

\frac{d P}{d t} = P (950 - P)

\frac{d y}{d x} = sin (x)

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