What is (\partial)/(\partial y)(x^2+y^2+10) ?

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

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(\partial)/(\partial y)(x^2+y^2+10)

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

2 y

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

\frac{\partial}{\partial y} (10) = 0

= 0 + 2 y + 0

Simplify

= 2 y

sin (7 x)

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

t^{2} y^{^{''}} + 11 t y^{^{'}} + 25 y = 0, y (1) = 4, y^{^{'}} (1) = 9

\int 18 - \frac{54}{15 - 2 x} d x

\frac{d}{d x} (\frac{( x ^{2} - 4 ) ^{2}}{( x ^{2} + 2 ) ^{3}})

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