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

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

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

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

3 y^{2} cos (2 x)

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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