What is (\partial)/(\partial y)(3x^2y+cos(y)) ?

The answer to (\partial)/(\partial y)(3x^2y+cos(y)) is 3x^2-sin(y)

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(\partial)/(\partial y)(3x^2y+cos(y))

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

3 x^{2} - sin (y)

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial y} (3 x^{2} y) + \frac{\partial}{\partial y} (cos (y))

\frac{\partial}{\partial y} (3 x^{2} y) = 3 x^{2}

\frac{\partial}{\partial y} (cos (y)) = - sin (y)

= 3 x^{2} - sin (y)

What is (\partial)/(\partial y)(3x^2y+cos(y)) ?
The answer to (\partial)/(\partial y)(3x^2y+cos(y)) is 3x^2-sin(y)