What is (\partial)/(\partial x)(y^2sin(x/y)) ?

The answer to (\partial)/(\partial x)(y^2sin(x/y)) is ycos(x/y)

Popular >

(\partial)/(\partial x)(y^2sin(x/y))

\frac{\partial}{\partial x} (y^{2} sin (\frac{x}{y}))

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

Solution steps

\frac{\partial}{\partial x} (y^{2} sin (\frac{x}{y}))

Treat

y

as a constant

Take the constant out:

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

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

Simplify

y^{2} cos (\frac{x}{y}) \frac{1}{y} : y cos (\frac{x}{y})

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

\frac{d}{d x} (\frac{i}{5 x ^{2} + 1})

y = \frac{2 x ^{2} + 4 x + 4}{x}

\int ln (4 - x) d x

\frac{d f ^{- 1}}{d x} f (x) = 3 x^{3} - 5 x^{2} - 2, x = 1272

\frac{1 + x}{1 + e ^{x}}

What is (\partial)/(\partial x)(y^2sin(x/y)) ?
The answer to (\partial)/(\partial x)(y^2sin(x/y)) is ycos(x/y)