What is (\partial)/(\partial y)(y^3sin(2x)) ?

The answer to (\partial)/(\partial y)(y^3sin(2x)) is 3y^2sin(2x)

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(\partial)/(\partial y)(y^3sin(2x))

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

3 y^{2} sin (2 x)

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

= sin (2 x) \cdot 3 y^{3 - 1}

Simplify

= 3 y^{2} sin (2 x)

\frac{d y}{d x} = 4

\frac{d}{d x} (4 x^{\frac{3}{5}})

\int_{1}^{2} (- 12 x + 6) d x

y^{^{'}} = \frac{x ^{2} - y ^{2}}{x y}, y (2) = 3

\int sin (3 x) cos (4 x) d x

What is (\partial)/(\partial y)(y^3sin(2x)) ?
The answer to (\partial)/(\partial y)(y^3sin(2x)) is 3y^2sin(2x)