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

The answer to (\partial)/(\partial x)(sin((x-y)/(x+y))) is (2ycos(\frac{x-y)/(x+y))}{(x+y)^2}

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

\int sin^{2} (8 x) cos^{2} (8 x) d x

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

\int \frac{1}{2 x 4 x ^{2} - 8} d x

\frac{\partial}{\partial x} (x^{n x y})

\frac{d}{d x} (9 x^{2})

What is (\partial)/(\partial x)(sin((x-y)/(x+y))) ?
The answer to (\partial)/(\partial x)(sin((x-y)/(x+y))) is (2ycos(\frac{x-y)/(x+y))}{(x+y)^2}