What is (\partial)/(\partial y)(sin(xy)+xsin(y)) ?

The answer to (\partial)/(\partial y)(sin(xy)+xsin(y)) is cos(xy)x+xcos(y)

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(\partial)/(\partial y)(sin(xy)+xsin(y))

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

cos (x y) x + x cos (y)

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= cos (x y) x + x cos (y)

x \to - 1 - lim ((x + 2 x^{3})^{4})

n = 0 \sum \infty (\frac{5}{5})^{n}

x y^{^{'}} + 5 y = x^{3} - x

\int \frac{x + 1}{x ^{2} - 2 x} d x

\frac{\partial}{\partial s} (s \cdot cos (t))

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