What is (\partial)/(\partial y)(x^3y+xcos(y)) ?

The answer to (\partial)/(\partial y)(x^3y+xcos(y)) is x^3-xsin(y)

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(\partial)/(\partial y)(x^3y+xcos(y))

\frac{\partial}{\partial y} (x^{3} y + x cos (y))

x^{3} - x sin (y)

Solution steps

\frac{\partial}{\partial y} (x^{3} y + x cos (y))

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (x^{3} y) + \frac{\partial}{\partial y} (x cos (y))

\frac{\partial}{\partial y} (x^{3} y) = x^{3}

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

= x^{3} - x sin (y)

\int_{- 4}^{4} 3 (16 - y^{2}) d y

\frac{d}{d x} (\frac{2 x ^{2} + x - 3}{2 x + 7})

\int x^{2} e^{2} d x

f (x) = x^{2} + 2, (3, 11)

\frac{d y}{d x} = (3 x)

What is (\partial)/(\partial y)(x^3y+xcos(y)) ?
The answer to (\partial)/(\partial y)(x^3y+xcos(y)) is x^3-xsin(y)