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

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

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(\partial)/(\partial y)(y^3sin(4x))

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

3 y^{2} sin (4 x)

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

\frac{d}{d x} ((1 + 6 x^{2}) (x - x^{2}))

\int x csch^{2} (\frac{x ^{2}}{2}) d x

x = 2 y^{2}, x = y^{2} + 4

\int (cos (x))^{6} d x

\frac{( x ^{2} - 1 )}{( x ^{2} + x + 1 )}

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