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

The answer to (\partial)/(\partial y)(ysin(x)y) is 2ysin(x)

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

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

2 y sin (x)

Solution steps

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

Simplify

y sin (x) y : y^{2} sin (x)

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= sin (x) \cdot 2 y^{2 - 1}

Simplify

= 2 y sin (x)

\frac{d}{d x} ((x - 0.1) (x - 0.5) (x - 0.6))

\frac{d}{d x} (x^{2} (6 - x)^{3})

\int \frac{1}{x ^{2} + 8 x + 20} d x

x \to 0 lim (\frac{4}{x} - \frac{4}{∣ x ∣})

y^{^{'}} + y = 5 sin (2 x)

What is (\partial)/(\partial y)(ysin(x)y) ?
The answer to (\partial)/(\partial y)(ysin(x)y) is 2ysin(x)