What is (\partial)/(\partial y)(y^5cos(3x)) ?

The answer to (\partial)/(\partial y)(y^5cos(3x)) is 5y^4cos(3x)

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(\partial)/(\partial y)(y^5cos(3x))

\frac{\partial}{\partial y} (y^{5} cos (3 x))

5 y^{4} cos (3 x)

Solution steps

\frac{\partial}{\partial y} (y^{5} cos (3 x))

Treat

x

as a constant

Take the constant out:

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

= cos (3 x) \frac{\partial}{\partial y} (y^{5})

Apply the Power Rule:

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

= cos (3 x) \cdot 5 y^{5 - 1}

Simplify

= 5 y^{4} cos (3 x)

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

\frac{( x ^{\frac{1}{3}} - 4 )}{x ^{\frac{7}{2}}}

\frac{d y}{d t} = t^{2}

y = \frac{csc ( x ^{2} )}{7 x - cos ^{2} ( x )}

2 t^{2} e^{t}

What is (\partial)/(\partial y)(y^5cos(3x)) ?
The answer to (\partial)/(\partial y)(y^5cos(3x)) is 5y^4cos(3x)