What is (\partial)/(\partial y)(cos(xy^2)) ?

The answer to (\partial)/(\partial y)(cos(xy^2)) is -sin(xy^2)*2xy

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(\partial)/(\partial y)(cos(xy^2))

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

- sin (x y^{2}) \cdot 2 x y

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (x y^{2}) = 2 x y

= - sin (x y^{2}) \cdot 2 x y

x \to - 2 lim (x - 1)

\int sin (x) d sin (x) d x

x \to 3 lim (x^{3} - x^{2} + 15)

y = 0, y = cos (x), [0, \frac{3 π}{2}]

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

What is (\partial)/(\partial y)(cos(xy^2)) ?
The answer to (\partial)/(\partial y)(cos(xy^2)) is -sin(xy^2)*2xy