What is (\partial}{\partial x}(830x-\frac{25000)/x-(5400)/y+2280y+457950) ?

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(\partial}{\partial x}(830x-\frac{25000)/x-(5400)/y+2280y+457950)

\frac{\partial}{\partial x} (830 x - \frac{25000}{x} - \frac{5400}{y} + 2280 y + 457950)

\frac{25000}{x ^{2}} + 830

Solution steps

\frac{\partial}{\partial x} (830 x - \frac{25000}{x} - \frac{5400}{y} + 2280 y + 457950)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (830 x) - \frac{\partial}{\partial x} (\frac{25000}{x}) - \frac{\partial}{\partial x} (\frac{5400}{y}) + \frac{\partial}{\partial x} (2280 y) + \frac{\partial}{\partial x} (457950)

\frac{\partial}{\partial x} (830 x) = 830

\frac{\partial}{\partial x} (\frac{25000}{x}) = - \frac{25000}{x ^{2}}

\frac{\partial}{\partial x} (\frac{5400}{y}) = 0

\frac{\partial}{\partial x} (2280 y) = 0

\frac{\partial}{\partial x} (457950) = 0

= 830 - (- \frac{25000}{x ^{2}}) - 0 + 0 + 0

Simplify

= \frac{25000}{x ^{2}} + 830

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What is (\partial}{\partial x}(830x-\frac{25000)/x-(5400)/y+2280y+457950) ?
The answer to (\partial}{\partial x}(830x-\frac{25000)/x-(5400)/y+2280y+457950) is (25000)/(x^2)+830