What is (\partial)/(\partial y)(3x^2+5y^2) ?

The answer to (\partial)/(\partial y)(3x^2+5y^2) is 10y

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(\partial)/(\partial y)(3x^2+5y^2)

\frac{\partial}{\partial y} (3 x^{2} + 5 y^{2})

10 y

Solution steps

\frac{\partial}{\partial y} (3 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} (3 x^{2}) + \frac{\partial}{\partial y} (5 y^{2})

\frac{\partial}{\partial y} (3 x^{2}) = 0

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

= 0 + 10 y

Simplify

= 10 y

x y^{^{'}} + y = - 2 x y^{2}, y (1) = 7

\frac{d}{d x} (lo g_{2} (x - 1) - 2)

y = x^{2} e^{x} - 2 x e^{x} + 6 e^{x}

f (x) = 16 x, at x = 16

(2 x^{- 2} + 3)^{- 3}

What is (\partial)/(\partial y)(3x^2+5y^2) ?
The answer to (\partial)/(\partial y)(3x^2+5y^2) is 10y