What is (\partial}{\partial y}(166x+456y-\frac{5000)/x-(1080)/y+43590) ?

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(\partial}{\partial y}(166x+456y-\frac{5000)/x-(1080)/y+43590)

\frac{\partial}{\partial y} (166 x + 456 y - \frac{5000}{x} - \frac{1080}{y} + 43590)

\frac{1080}{y ^{2}} + 456

Solution steps

\frac{\partial}{\partial y} (166 x + 456 y - \frac{5000}{x} - \frac{1080}{y} + 43590)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (166 x) + \frac{\partial}{\partial y} (456 y) - \frac{\partial}{\partial y} (\frac{5000}{x}) - \frac{\partial}{\partial y} (\frac{1080}{y}) + \frac{\partial}{\partial y} (43590)

\frac{\partial}{\partial y} (166 x) = 0

\frac{\partial}{\partial y} (456 y) = 456

\frac{\partial}{\partial y} (\frac{5000}{x}) = 0

\frac{\partial}{\partial y} (\frac{1080}{y}) = - \frac{1080}{y ^{2}}

\frac{\partial}{\partial y} (43590) = 0

= 0 + 456 - 0 - (- \frac{1080}{y ^{2}}) + 0

Simplify

= \frac{1080}{y ^{2}} + 456

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f (x) = \frac{64}{x ^{2} + 16}, at x = - 4

5 e^{- t}

\frac{d}{d x} (arcsin (x))

x \to - 1 lim (1 - x^{2})

What is (\partial}{\partial y}(166x+456y-\frac{5000)/x-(1080)/y+43590) ?
The answer to (\partial}{\partial y}(166x+456y-\frac{5000)/x-(1080)/y+43590) is (1080)/(y^2)+456