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

The answer to (\partial)/(\partial x)(x^2sin(x/y)) is 2xsin(x/y)+(x^2cos(x/y))/y

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = sin (\frac{x}{y})

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

\frac{\partial}{\partial x} (x^{2}) = 2 x

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

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

Multiply fractions:

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

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

\int_{0}^{1} 16 \frac{1}{x ^{p}} d x

x - x^{3} (1)

\int 7 arctan (x) d x

f (x) = \frac{1}{x} + 200

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