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

The answer to (\partial)/(\partial y)(3y^2cos(4x)) is 6ycos(4x)

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(\partial)/(\partial y)(3y^2cos(4x))

\frac{\partial}{\partial y} (3 y^{2} cos (4 x))

6 y cos (4 x)

Solution steps

\frac{\partial}{\partial y} (3 y^{2} cos (4 x))

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

= 3 cos (4 x) \cdot 2 y^{2 - 1}

Simplify

= 6 y cos (4 x)

What is (\partial)/(\partial y)(3y^2cos(4x)) ?
The answer to (\partial)/(\partial y)(3y^2cos(4x)) is 6ycos(4x)