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

The answer to (\partial)/(\partial y)(xy^2+5) is 2xy

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

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

2 x y

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial y} (5) = 0

= 2 x y + 0

Simplify

= 2 x y

\int \frac{x}{( x ^{2} + 1 ) ^{\frac{5}{2}}} d x

\int \frac{y ^{3}}{y ^{4} + 1} d y

(x^{2} + 1) y^{^{'}} + 3 x (y - 1) = 0, y (0) = 8

\int \frac{sin ( c x )}{cos ^{2} ( c x )} d x

\frac{14 x + 8 x ^{2}}{( 7 + 8 x ) ^{2}}

What is (\partial)/(\partial y)(xy^2+5) ?
The answer to (\partial)/(\partial y)(xy^2+5) is 2xy