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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

= cos (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}

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

\frac{d}{d x} (cosh (x) cos (x^{2}))

\frac{d}{d x} (arctan (\frac{8}{x}))

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

a re a y = - x^{2} + 16, y = \frac{- x}{4} - 1, 4 (y + 6.5) = 6.5 x

d er i v a t i v e (3 x^{2} - 6 x + 6) e^{- 5 x}

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