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

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

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

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

4 y^{3} cos (2 x)

Solution steps

\frac{\partial}{\partial y} (y^{4} 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^{4})

Apply the Power Rule:

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

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

Simplify

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

y = x^{0.85}

\frac{d v}{d t} = - b v

(x + 2)^{3}

x^{^{''}} = t^{- 4}

n = 2 \sum \infty \frac{4}{ln ( n ^{3} )}

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