What is (\partial)/(\partial x)(ysin(x/y)) ?

The answer to (\partial)/(\partial x)(ysin(x/y)) is cos(x/y)

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(\partial)/(\partial x)(ysin(x/y))

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

cos (\frac{x}{y})

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

f (x) = \frac{x ^{2} - 6 x + 1}{x ^{2} + 4}

\int (x + 3)^{2} (2 - x)^{5} d x

y^{^{''}} + 6 y + 9 = 0, y (0) = - 3, y^{^{'}} (0) = - 1

\int 4 x^{4} d x

\frac{\partial}{\partial z} (x e^{y} + y e^{z} - z e^{x})

What is (\partial)/(\partial x)(ysin(x/y)) ?
The answer to (\partial)/(\partial x)(ysin(x/y)) is cos(x/y)