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

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

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

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

y^{3} cos (4 x) \cdot 4

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

cos (4 x) \frac{\partial}{\partial x} (4 x)

= cos (4 x) \frac{\partial}{\partial x} (4 x)

\frac{\partial}{\partial x} (4 x) = 4

= y^{3} cos (4 x) \cdot 4

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