What is the derivative of (5/x+x(5/x-x)) ?

The derivative of (5/x+x(5/x-x)) is -2x-(50)/(x^3)

What is the first derivative of (5/x+x(5/x-x)) ?

The first derivative of (5/x+x(5/x-x)) is -2x-(50)/(x^3)

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\frac{d}{d x} ((\frac{5}{x} + x) (\frac{5}{x} - x))

- 2 x - \frac{50}{x ^{3}}

Solution steps

\frac{d}{d x} ((\frac{5}{x} + x) (\frac{5}{x} - x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = \frac{5}{x} + x, g = \frac{5}{x} - x

= \frac{d}{d x} (\frac{5}{x} + x) (\frac{5}{x} - x) + \frac{d}{d x} (\frac{5}{x} - x) (\frac{5}{x} + x)

\frac{d}{d x} (\frac{5}{x} + x) = - \frac{5}{x ^{2}} + 1

\frac{d}{d x} (\frac{5}{x} - x) = - \frac{5}{x ^{2}} - 1

= (- \frac{5}{x ^{2}} + 1) (\frac{5}{x} - x) + (- \frac{5}{x ^{2}} - 1) (\frac{5}{x} + x)

Simplify

(- \frac{5}{x ^{2}} + 1) (\frac{5}{x} - x) + (- \frac{5}{x ^{2}} - 1) (\frac{5}{x} + x) : - 2 x - \frac{50}{x ^{3}}

= - 2 x - \frac{50}{x ^{3}}

y^{^{'}} = (x - 2) e^{- 2 y}

\int \frac{1}{9 e ^{- 6 x} + e ^{6 x}} d x

3 y^{^{''}} + 27 y = 0

d er i v a t i v e \frac{32}{x}

\frac{\partial}{\partial x} (e^{x} - e^{x^{2}})

What is the derivative of (5/x+x(5/x-x)) ?
The derivative of (5/x+x(5/x-x)) is -2x-(50)/(x^3)
What is the first derivative of (5/x+x(5/x-x)) ?
The first derivative of (5/x+x(5/x-x)) is -2x-(50)/(x^3)