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)

\int \frac{x ^{2} - 121}{x} d x

k = 1 \sum \infty \frac{( - 1 ) ^{k} \cdot ( 1 ) ^{(3 \cdot k)}}{k}

\int x y (x + y) d y

n = 0 \sum \infty \frac{2 ^{n}}{n !}

x (x - 2) y^{^{'}} + 2 y = 0

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