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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

\frac{d}{d x} (3 x + 6)

y^{^{'}} - 3 y = 6

f (x) = cos (sin (x^{2}))

\int (x + 1)^{- 3} d x

\int \frac{x ^{2}}{x ^{3} - 2} d x

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