What is (\partial)/(\partial y)(sin(x*y^2)) ?

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

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(\partial)/(\partial y)(sin(x*y^2))

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

cos (x y^{2}) \cdot 2 x y

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

= cos (x y^{2}) \cdot 2 x y

\frac{d}{d x} (sec^{2} (m θ))

x \to 0 lim (x + \frac{2 x ^{2} + x}{x})

\frac{d}{d x} (\frac{x + 5}{2 x ^{2} e ^{x}})

\int 1 - 36 x^{2} d x

f (x) = x + 24, (1, 5)

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