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

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

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

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

10 y

Solution steps

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

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} (5 y^{2})

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

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

= 0 + 10 y

Simplify

= 10 y

x \to 3 - lim (- \frac{3}{7} x + \frac{4}{11})

\frac{\partial}{\partial z} (\frac{x}{y + z})

x \to 0 - lim (\frac{( x + 4 )}{( 3 )})

9 y^{^{''}} - 30 y^{^{'}} + 25 y = 0

\int \frac{2}{5} x^{\frac{5}{2}} - \frac{54}{5} d x

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