What is (\partial)/(\partial y)(y^3cos(4x)) ?

The answer to (\partial)/(\partial y)(y^3cos(4x)) is 3y^2cos(4x)

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(\partial)/(\partial y)(y^3cos(4x))

\frac{\partial}{\partial y} (y^{3} cos (4 x))

3 y^{2} cos (4 x)

Solution steps

\frac{\partial}{\partial y} (y^{3} cos (4 x))

Treat

x

as a constant

Take the constant out:

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

= cos (4 x) \frac{\partial}{\partial y} (y^{3})

Apply the Power Rule:

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

= cos (4 x) \cdot 3 y^{3 - 1}

Simplify

= 3 y^{2} cos (4 x)

\frac{d}{d x} ((1 + 4 x^{2}) (x - x^{2}))

\int x - y^{3} + y^{2} sin (x) d x

(1 + x)^{- \frac{2}{5}}

\int e^{- k x} cos (w x) d x

3 y^{^{''}} - 6 y^{^{'}} + 30 y = e^{x} tan (3 x)

What is (\partial)/(\partial y)(y^3cos(4x)) ?
The answer to (\partial)/(\partial y)(y^3cos(4x)) is 3y^2cos(4x)