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

The answer to (\partial)/(\partial x)(sin(4x^3y-5xy^4)) is cos(4x^3y-5xy^4)(12yx^2-5y^4)

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

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

cos (4 x^{3} y - 5 x y^{4}) (12 y x^{2} - 5 y^{4})

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (4 x^{3} y - 5 x y^{4}) = 12 y x^{2} - 5 y^{4}

= cos (4 x^{3} y - 5 x y^{4}) (12 y x^{2} - 5 y^{4})

x \to 4 lim (7^{x} + 12 x)

\int x^{3} (a^{2} + x^{2})^{\frac{1}{2}} d x

y = 6^{x}

y = 7 x, (7, 7)

\int \frac{x}{3 x ^{2} + 4} d x

What is (\partial)/(\partial x)(sin(4x^3y-5xy^4)) ?
The answer to (\partial)/(\partial x)(sin(4x^3y-5xy^4)) is cos(4x^3y-5xy^4)(12yx^2-5y^4)