What is (\partial)/(\partial x)(sin(4x^3y-6xy^2)) ?

The answer to (\partial)/(\partial x)(sin(4x^3y-6xy^2)) is cos(4x^3y-6xy^2)(12yx^2-6y^2)

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(\partial)/(\partial x)(sin(4x^3y-6xy^2))

\frac{\partial}{\partial x} (sin (4 x^{3} y - 6 x y^{2}))

cos (4 x^{3} y - 6 x y^{2}) (12 y x^{2} - 6 y^{2})

Solution steps

\frac{\partial}{\partial x} (sin (4 x^{3} y - 6 x y^{2}))

Treat

y

as a constant

Apply the chain rule:

cos (4 x^{3} y - 6 x y^{2}) \frac{\partial}{\partial x} (4 x^{3} y - 6 x y^{2})

= cos (4 x^{3} y - 6 x y^{2}) \frac{\partial}{\partial x} (4 x^{3} y - 6 x y^{2})

\frac{\partial}{\partial x} (4 x^{3} y - 6 x y^{2}) = 12 y x^{2} - 6 y^{2}

= cos (4 x^{3} y - 6 x y^{2}) (12 y x^{2} - 6 y^{2})

\frac{d}{d x} (2 (e^{3 x} + 3 e^{3 x} x))

(7.7) (12.11)

x \to 0 lim (\frac{x ^{3} + 4}{x - 2})

\int x 5 x - 2 d x

\int - 2 sin (x) d x

What is (\partial)/(\partial x)(sin(4x^3y-6xy^2)) ?
The answer to (\partial)/(\partial x)(sin(4x^3y-6xy^2)) is cos(4x^3y-6xy^2)(12yx^2-6y^2)