What is (\partial}{\partial x}(ln(x/y)+\frac{z-x)/x) ?

The answer to (\partial}{\partial x}(ln(x/y)+\frac{z-x)/x) is 1/x-z/(x^2)

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(\partial}{\partial x}(ln(x/y)+\frac{z-x)/x)

\frac{\partial}{\partial x} (ln (\frac{x}{y}) + \frac{z - x}{x})

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

Solution steps

\frac{\partial}{\partial x} (ln (\frac{x}{y}) + \frac{z - x}{x})

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (ln (\frac{x}{y})) + \frac{\partial}{\partial x} (\frac{z - x}{x})

\frac{\partial}{\partial x} (ln (\frac{x}{y})) = \frac{1}{x}

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

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

f (x) = 2 x^{2} - 9 x + 10

\int \frac{x - 3}{x} d x

x \to \infty lim (\frac{e ^{x^{2}}}{5 - x ^{3}})

\frac{d y}{d x} = y x^{2} + y x, y (0) = - 1

What is (\partial}{\partial x}(ln(x/y)+\frac{z-x)/x) ?
The answer to (\partial}{\partial x}(ln(x/y)+\frac{z-x)/x) is 1/x-z/(x^2)