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

The answer to (\partial)/(\partial y)(5xy^2+x^2) is 10xy

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

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

10 x y

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (5 x y^{2}) = 10 x y

\frac{\partial}{\partial y} (x^{2}) = 0

= 10 x y + 0

Simplify

= 10 x y

t^{2} y^{^{''}} + t y^{^{'}} + 64 y = 0

\frac{d}{d v} (\frac{m}{v})

1 - 2 x

t \to 1 + lim (\frac{4}{( t - 1 ) ^{3}})

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

What is (\partial)/(\partial y)(5xy^2+x^2) ?
The answer to (\partial)/(\partial y)(5xy^2+x^2) is 10xy