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

The answer to (\partial)/(\partial y)(-3y^4sin(3x)) is -12y^3sin(3x)

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

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

- 12 y^{3} sin (3 x)

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= - 12 y^{3} sin (3 x)

What is (\partial)/(\partial y)(-3y^4sin(3x)) ?
The answer to (\partial)/(\partial y)(-3y^4sin(3x)) is -12y^3sin(3x)