What is (\partial)/(\partial x)(sin(5x^4y-3xy^4)) ?

The answer to (\partial)/(\partial x)(sin(5x^4y-3xy^4)) is cos(5x^4y-3xy^4)(20yx^3-3y^4)

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(\partial)/(\partial x)(sin(5x^4y-3xy^4))

\frac{\partial}{\partial x} (sin (5 x^{4} y - 3 x y^{4}))

cos (5 x^{4} y - 3 x y^{4}) (20 y x^{3} - 3 y^{4})

Solution steps

\frac{\partial}{\partial x} (sin (5 x^{4} y - 3 x y^{4}))

Treat

y

as a constant

Apply the chain rule:

cos (5 x^{4} y - 3 x y^{4}) \frac{\partial}{\partial x} (5 x^{4} y - 3 x y^{4})

= cos (5 x^{4} y - 3 x y^{4}) \frac{\partial}{\partial x} (5 x^{4} y - 3 x y^{4})

\frac{\partial}{\partial x} (5 x^{4} y - 3 x y^{4}) = 20 y x^{3} - 3 y^{4}

= cos (5 x^{4} y - 3 x y^{4}) (20 y x^{3} - 3 y^{4})

What is (\partial)/(\partial x)(sin(5x^4y-3xy^4)) ?
The answer to (\partial)/(\partial x)(sin(5x^4y-3xy^4)) is cos(5x^4y-3xy^4)(20yx^3-3y^4)