What is (\partial)/(\partial y)(5cos(xy^2)) ?

The answer to (\partial)/(\partial y)(5cos(xy^2)) is -10xysin(xy^2)

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(\partial)/(\partial y)(5cos(xy^2))

\frac{\partial}{\partial y} (5 cos (x y^{2}))

- 10 x y sin (x y^{2})

Solution steps

\frac{\partial}{\partial y} (5 cos (x y^{2}))

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{\partial}{\partial y} (cos (x y^{2}))

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

= 5 (- sin (x y^{2}) \cdot 2 x y)

Simplify

= - 10 x y sin (x y^{2})

What is (\partial)/(\partial y)(5cos(xy^2)) ?
The answer to (\partial)/(\partial y)(5cos(xy^2)) is -10xysin(xy^2)