What is (\partial)/(\partial x)(5/(xy)-4x^2-2y^2) ?

The answer to (\partial)/(\partial x)(5/(xy)-4x^2-2y^2) is -8x-5/(x^2y)

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(\partial)/(\partial x)(5/(xy)-4x^2-2y^2)

\frac{\partial}{\partial x} (\frac{5}{x y} - 4 x^{2} - 2 y^{2})

- 8 x - \frac{5}{x ^{2} y}

Solution steps

\frac{\partial}{\partial x} (\frac{5}{x y} - 4 x^{2} - 2 y^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (\frac{5}{x y}) - \frac{\partial}{\partial x} (4 x^{2}) - \frac{\partial}{\partial x} (2 y^{2})

\frac{\partial}{\partial x} (\frac{5}{x y}) = - \frac{5}{y x ^{2}}

\frac{\partial}{\partial x} (4 x^{2}) = 8 x

\frac{\partial}{\partial x} (2 y^{2}) = 0

= - \frac{5}{y x ^{2}} - 8 x - 0

Simplify

= - 8 x - \frac{5}{x ^{2} y}

\int \frac{1}{x ^{2} - 4 x + 8} d x

f (x) = (x)^{3}

x \to 0 lim (\frac{( x + 1 ) ^{2} - 1}{x})

y^{^{'}} = 6 x + y, y (0) = 8

\int_{0}^{l n (2)} e^{- x} d x

What is (\partial)/(\partial x)(5/(xy)-4x^2-2y^2) ?
The answer to (\partial)/(\partial x)(5/(xy)-4x^2-2y^2) is -8x-5/(x^2y)