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

The answer to (\partial)/(\partial x)(sin(x/(1+y))) is (cos(x/(1+y)))/(1+y)

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

cos (\frac{x}{1 + y}) \frac{1}{1 + y} : \frac{cos ( \frac{x}{1 + y} )}{1 + y}

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

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

\frac{d}{d x} (1 - cos (x))

\int sin (9 t) sin (4 t) d t

What is (\partial)/(\partial x)(sin(x/(1+y))) ?
The answer to (\partial)/(\partial x)(sin(x/(1+y))) is (cos(x/(1+y)))/(1+y)