What is (\partial)/(\partial y)(y^4sin(6x)) ?

The answer to (\partial)/(\partial y)(y^4sin(6x)) is 4y^3sin(6x)

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(\partial)/(\partial y)(y^4sin(6x))

\frac{\partial}{\partial y} (y^{4} sin (6 x))

4 y^{3} sin (6 x)

Solution steps

\frac{\partial}{\partial y} (y^{4} sin (6 x))

Treat

x

as a constant

Take the constant out:

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

= sin (6 x) \frac{\partial}{\partial y} (y^{4})

Apply the Power Rule:

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

= sin (6 x) \cdot 4 y^{4 - 1}

Simplify

= 4 y^{3} sin (6 x)

\int \frac{1}{u ( u + 2 )} d u

2 x^{2} + x - 1

y^{^{''}} + 4 y = 4 cos (2 t)

\int \frac{9}{( 7 x + 4 ) ^{5}} d x

\int 2 x^{2} cos (5 x) d x

What is (\partial)/(\partial y)(y^4sin(6x)) ?
The answer to (\partial)/(\partial y)(y^4sin(6x)) is 4y^3sin(6x)