What is (\partial)/(\partial y)(y^5cos(2x)) ?

The answer to (\partial)/(\partial y)(y^5cos(2x)) is 5y^4cos(2x)

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(\partial)/(\partial y)(y^5cos(2x))

\frac{\partial}{\partial y} (y^{5} cos (2 x))

5 y^{4} cos (2 x)

Solution steps

\frac{\partial}{\partial y} (y^{5} 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^{5})

Apply the Power Rule:

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

= cos (2 x) \cdot 5 y^{5 - 1}

Simplify

= 5 y^{4} cos (2 x)

\int \frac{3 x ^{2}}{x ^{3} + 8} d x

\int x^{2} sin (π) x d x

\frac{d y}{d x} = \frac{y}{3} + 3 x + 7

\int (- 8 cos (- 2)) ddd

\int \frac{1}{x ^{4} x ^{2} + 5} d x

What is (\partial)/(\partial y)(y^5cos(2x)) ?
The answer to (\partial)/(\partial y)(y^5cos(2x)) is 5y^4cos(2x)