What is (\partial)/(\partial x)(sin(6x^3y-6xy^2)) ?

The answer to (\partial)/(\partial x)(sin(6x^3y-6xy^2)) is cos(6x^3y-6xy^2)(18yx^2-6y^2)

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(\partial)/(\partial x)(sin(6x^3y-6xy^2))

\frac{\partial}{\partial x} (sin (6 x^{3} y - 6 x y^{2}))

cos (6 x^{3} y - 6 x y^{2}) (18 y x^{2} - 6 y^{2})

Solution steps

\frac{\partial}{\partial x} (sin (6 x^{3} y - 6 x y^{2}))

Treat

y

as a constant

Apply the chain rule:

cos (6 x^{3} y - 6 x y^{2}) \frac{\partial}{\partial x} (6 x^{3} y - 6 x y^{2})

= cos (6 x^{3} y - 6 x y^{2}) \frac{\partial}{\partial x} (6 x^{3} y - 6 x y^{2})

\frac{\partial}{\partial x} (6 x^{3} y - 6 x y^{2}) = 18 y x^{2} - 6 y^{2}

= cos (6 x^{3} y - 6 x y^{2}) (18 y x^{2} - 6 y^{2})

\frac{d}{d x} (\frac{7}{x ^{8} + 5 x + 1})

\frac{d}{d x} (sin (14 x))

y^{^{'}} = 1 + y^{2} + x + x y^{2}

\int \frac{( 1 + x )}{x} d x

x \to 0 lim (2 x + 12)

What is (\partial)/(\partial x)(sin(6x^3y-6xy^2)) ?
The answer to (\partial)/(\partial x)(sin(6x^3y-6xy^2)) is cos(6x^3y-6xy^2)(18yx^2-6y^2)