What is (\partial}{\partial x}(xy+\frac{27)/x) ?

The answer to (\partial}{\partial x}(xy+\frac{27)/x) is y-(27)/(x^2)

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(\partial}{\partial x}(xy+\frac{27)/x)

\frac{\partial}{\partial x} (x y + \frac{27}{x})

y - \frac{27}{x ^{2}}

Solution steps

\frac{\partial}{\partial x} (x y + \frac{27}{x})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x y) + \frac{\partial}{\partial x} (\frac{27}{x})

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

\frac{\partial}{\partial x} (\frac{27}{x}) = - \frac{27}{x ^{2}}

= y - \frac{27}{x ^{2}}

\frac{d}{d x} (e^{5 x + πi})

\int (6 + x^{5})^{2} 5 x^{4} d x

\frac{\partial}{\partial x} (- cos (2 x))

\frac{\partial}{\partial x} (x^{3} + y^{3} - 3 x^{2} + 3 y^{2})

\frac{d}{d a} (1 + cos^{4} (a) - sin^{4} (a))

What is (\partial}{\partial x}(xy+\frac{27)/x) ?
The answer to (\partial}{\partial x}(xy+\frac{27)/x) is y-(27)/(x^2)