What is (\partial)/(\partial x)(sin(3x^3y-5xy^3)) ?

The answer to (\partial)/(\partial x)(sin(3x^3y-5xy^3)) is cos(3x^3y-5xy^3)(9yx^2-5y^3)

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(\partial)/(\partial x)(sin(3x^3y-5xy^3))

\frac{\partial}{\partial x} (sin (3 x^{3} y - 5 x y^{3}))

cos (3 x^{3} y - 5 x y^{3}) (9 y x^{2} - 5 y^{3})

Solution steps

\frac{\partial}{\partial x} (sin (3 x^{3} y - 5 x y^{3}))

Treat

y

as a constant

Apply the chain rule:

cos (3 x^{3} y - 5 x y^{3}) \frac{\partial}{\partial x} (3 x^{3} y - 5 x y^{3})

= cos (3 x^{3} y - 5 x y^{3}) \frac{\partial}{\partial x} (3 x^{3} y - 5 x y^{3})

\frac{\partial}{\partial x} (3 x^{3} y - 5 x y^{3}) = 9 y x^{2} - 5 y^{3}

= cos (3 x^{3} y - 5 x y^{3}) (9 y x^{2} - 5 y^{3})

What is (\partial)/(\partial x)(sin(3x^3y-5xy^3)) ?
The answer to (\partial)/(\partial x)(sin(3x^3y-5xy^3)) is cos(3x^3y-5xy^3)(9yx^2-5y^3)