What is (\partial)/(\partial x)(cos(7x^2y-3xy^3)) ?

The answer to (\partial)/(\partial x)(cos(7x^2y-3xy^3)) is -sin(7x^2y-3xy^3)(14yx-3y^3)

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(\partial)/(\partial x)(cos(7x^2y-3xy^3))

\frac{\partial}{\partial x} (cos (7 x^{2} y - 3 x y^{3}))

- sin (7 x^{2} y - 3 x y^{3}) (14 y x - 3 y^{3})

Solution steps

\frac{\partial}{\partial x} (cos (7 x^{2} y - 3 x y^{3}))

Treat

y

as a constant

Apply the chain rule:

- sin (7 x^{2} y - 3 x y^{3}) \frac{\partial}{\partial x} (7 x^{2} y - 3 x y^{3})

= - sin (7 x^{2} y - 3 x y^{3}) \frac{\partial}{\partial x} (7 x^{2} y - 3 x y^{3})

\frac{\partial}{\partial x} (7 x^{2} y - 3 x y^{3}) = 14 y x - 3 y^{3}

= - sin (7 x^{2} y - 3 x y^{3}) (14 y x - 3 y^{3})

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

4 x, x^{2}, 3

cos (9 x)

y = \frac{x}{x + 3}

\frac{d}{d x} (- a e^{- x})

What is (\partial)/(\partial x)(cos(7x^2y-3xy^3)) ?
The answer to (\partial)/(\partial x)(cos(7x^2y-3xy^3)) is -sin(7x^2y-3xy^3)(14yx-3y^3)