What is (\partial)/(\partial x)((x-7)^2+(y-1)^2+29) ?

The answer to (\partial)/(\partial x)((x-7)^2+(y-1)^2+29) is 2x-14

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(\partial)/(\partial x)((x-7)^2+(y-1)^2+29)

\frac{\partial}{\partial x} ((x - 7)^{2} + (y - 1)^{2} + 29)

2 x - 14

Solution steps

\frac{\partial}{\partial x} ((x - 7)^{2} + (y - 1)^{2} + 29)

Simplify

(x - 7)^{2} + (y - 1)^{2} + 29 : x^{2} - 14 x + y^{2} + 79 - 2 y

= \frac{\partial}{\partial x} (x^{2} - 14 x + y^{2} + 79 - 2 y)

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} (14 x) + \frac{\partial}{\partial x} (y^{2}) + \frac{\partial}{\partial x} (79) - \frac{\partial}{\partial x} (2 y)

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

\frac{\partial}{\partial x} (14 x) = 14

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

\frac{\partial}{\partial x} (79) = 0

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

= 2 x - 14 + 0 + 0 - 0

Simplify

= 2 x - 14

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

n \to \infty lim (i = 3 \sum 8 (i + 1)^{2})

\int \frac{1}{11 - x ^{2}} d x

\int (\frac{3}{x ^{7}}) d x

\int \frac{( x ^{5} + 2 )}{x ^{2} - 1} d x

What is (\partial)/(\partial x)((x-7)^2+(y-1)^2+29) ?
The answer to (\partial)/(\partial x)((x-7)^2+(y-1)^2+29) is 2x-14