What is (\partial)/(\partial x)((x+2)^2-2(y-4)^2+1) ?

The answer to (\partial)/(\partial x)((x+2)^2-2(y-4)^2+1) is 2x+4

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(\partial)/(\partial x)((x+2)^2-2(y-4)^2+1)

\frac{\partial}{\partial x} ((x + 2)^{2} - 2 (y - 4)^{2} + 1)

2 x + 4

Solution steps

\frac{\partial}{\partial x} ((x + 2)^{2} - 2 (y - 4)^{2} + 1)

Simplify

(x + 2)^{2} - 2 (y - 4)^{2} + 1 : x^{2} + 4 x + 16 y - 2 y^{2} - 27

= \frac{\partial}{\partial x} (x^{2} + 4 x + 16 y - 2 y^{2} - 27)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{2}) + \frac{\partial}{\partial x} (4 x) + \frac{\partial}{\partial x} (16 y) - \frac{\partial}{\partial x} (2 y^{2}) - \frac{\partial}{\partial x} (27)

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

\frac{\partial}{\partial x} (4 x) = 4

\frac{\partial}{\partial x} (16 y) = 0

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

\frac{\partial}{\partial x} (27) = 0

= 2 x + 4 + 0 - 0 - 0

Simplify

= 2 x + 4

What is (\partial)/(\partial x)((x+2)^2-2(y-4)^2+1) ?
The answer to (\partial)/(\partial x)((x+2)^2-2(y-4)^2+1) is 2x+4