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

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

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

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

\frac{1}{y - 2} - \frac{1}{x ^{2}}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (\frac{1}{x}) = - \frac{1}{x ^{2}}

= \frac{1}{y - 2} - \frac{1}{x ^{2}}

\int \frac{4 - 3 cos ( x )}{sin ^{2} ( x )} d x

x \to 0 lim (\frac{8 e ^{2 x} - 8 e ^{- 4 x} - 36 x - 6}{3 x ^{2} + 4 x})

\int - x^{n} d x

x^{2} - 8 x - 5

\int \frac{x + 3}{x ^{2} + 16} d x

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