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)

(\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})

d er i v a t i v e cos (9 x)

\frac{\partial ^{2}}{\partial y ^{2}} (x^{2} - e^{y^{2}})

\int_{0}^{\frac{π}{8}} x tan^{2} (2 x) d x

\int \frac{1}{4 u ^{2} + 9 - 41 u} d u

l a pl a ce t r an s f or m - sin (2 t)

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)