What is (\partial)/(\partial y)(-2sin(y)+xy^3) ?

The answer to (\partial)/(\partial y)(-2sin(y)+xy^3) is -2cos(y)+3xy^2

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(\partial)/(\partial y)(-2sin(y)+xy^3)

\frac{\partial}{\partial y} (- 2 sin (y) + x y^{3})

- 2 cos (y) + 3 x y^{2}

Solution steps

\frac{\partial}{\partial y} (- 2 sin (y) + x y^{3})

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= - \frac{\partial}{\partial y} (2 sin (y)) + \frac{\partial}{\partial y} (x y^{3})

\frac{\partial}{\partial y} (2 sin (y)) = 2 cos (y)

\frac{\partial}{\partial y} (x y^{3}) = 3 x y^{2}

= - 2 cos (y) + 3 x y^{2}

\int \frac{1}{( 225 + x ^{2} ) ^{\frac{3}{2}}} d x

\int e^{x} (3 e^{x} - 2)^{2} d x

\frac{d}{d x} (ln (8 x + 7))

\int \frac{20}{e ^{\frac{x}{5}}} d x

f (x) = \frac{12 - 8 x}{5 x ^{\frac{2}{5}}}

What is (\partial)/(\partial y)(-2sin(y)+xy^3) ?
The answer to (\partial)/(\partial y)(-2sin(y)+xy^3) is -2cos(y)+3xy^2