What is (\partial)/(\partial y)(x^2-y^3+5x+12y+1) ?

The answer to (\partial)/(\partial y)(x^2-y^3+5x+12y+1) is -3y^2+12

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(\partial)/(\partial y)(x^2-y^3+5x+12y+1)

\frac{\partial}{\partial y} (x^{2} - y^{3} + 5 x + 12 y + 1)

- 3 y^{2} + 12

Solution steps

\frac{\partial}{\partial y} (x^{2} - y^{3} + 5 x + 12 y + 1)

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^{3}) + \frac{\partial}{\partial y} (5 x) + \frac{\partial}{\partial y} (12 y) + \frac{\partial}{\partial y} (1)

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

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

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

\frac{\partial}{\partial y} (12 y) = 12

\frac{\partial}{\partial y} (1) = 0

= 0 - 3 y^{2} + 0 + 12 + 0

Simplify

= - 3 y^{2} + 12

What is (\partial)/(\partial y)(x^2-y^3+5x+12y+1) ?
The answer to (\partial)/(\partial y)(x^2-y^3+5x+12y+1) is -3y^2+12