What is (\partial)/(\partial x)(sin(4x^2y-4xy^3)) ?

The answer to (\partial)/(\partial x)(sin(4x^2y-4xy^3)) is cos(4x^2y-4xy^3)(8yx-4y^3)

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(\partial)/(\partial x)(sin(4x^2y-4xy^3))

\frac{\partial}{\partial x} (sin (4 x^{2} y - 4 x y^{3}))

cos (4 x^{2} y - 4 x y^{3}) (8 y x - 4 y^{3})

Solution steps

\frac{\partial}{\partial x} (sin (4 x^{2} y - 4 x y^{3}))

Treat

y

as a constant

Apply the chain rule:

cos (4 x^{2} y - 4 x y^{3}) \frac{\partial}{\partial x} (4 x^{2} y - 4 x y^{3})

= cos (4 x^{2} y - 4 x y^{3}) \frac{\partial}{\partial x} (4 x^{2} y - 4 x y^{3})

\frac{\partial}{\partial x} (4 x^{2} y - 4 x y^{3}) = 8 y x - 4 y^{3}

= cos (4 x^{2} y - 4 x y^{3}) (8 y x - 4 y^{3})

What is (\partial)/(\partial x)(sin(4x^2y-4xy^3)) ?
The answer to (\partial)/(\partial x)(sin(4x^2y-4xy^3)) is cos(4x^2y-4xy^3)(8yx-4y^3)