What is the derivative of 1/(x(x-1)) ?

The derivative of 1/(x(x-1)) is -(2x-1)/(x^2(x-1)^2)

What is the first derivative of 1/(x(x-1)) ?

The first derivative of 1/(x(x-1)) is -(2x-1)/(x^2(x-1)^2)

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\frac{d}{d x} (\frac{1}{x ( x - 1 )})

- \frac{2 x - 1}{x ^{2} ( x - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{x ( x - 1 )})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

- \frac{1}{( x ( x - 1 ) ) ^{2}} (2 x - 1) : - \frac{2 x - 1}{x ^{2} ( x - 1 ) ^{2}}

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

x \frac{d y}{d x} = 6 y

f (x) = 2 x^{2} + x - 3, at x = - 1

y^{^{'}} = (t + y)^{2}

2 x, 3 x^{2}, 0, 1

\frac{d y}{d t} = \frac{t e ^{t}}{y 6 + y ^{2}}

What is the derivative of 1/(x(x-1)) ?
The derivative of 1/(x(x-1)) is -(2x-1)/(x^2(x-1)^2)
What is the first derivative of 1/(x(x-1)) ?
The first derivative of 1/(x(x-1)) is -(2x-1)/(x^2(x-1)^2)