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

The answer to (\partial)/(\partial y)(y^2sin(xy)) is 2ysin(xy)+cos(xy)xy^2

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the Product Rule:

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

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

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

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

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

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

x \to 5 lim (\frac{2}{( x - 5 ) ^{6}})

x \to 1 lim (2 x^{- 1})

t e^{- 5 t} sin (5 t)

\int 6 e^{7} d x

\frac{d}{d x} (e^{2 x} + 3)

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