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Popular >

derivative of-x/(x-1)

Solution

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

Solution

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

Popular Examples

limit as x approaches 0 of (9cos(x)-9)/x

x \to 0 lim (\frac{9 cos ( x ) - 9}{x})

derivative of (x-6/(3x-2))

\frac{d}{d x} (\frac{x - 6}{3 x - 2})

derivative of y=(x^5+2)^2(x^3+4)^4 derivative of

y = (x^{5} + 2)^{2} (x^{3} + 4)^{4}

derivative of 1/2 ln(x^2+y^2)

\frac{d}{d x} (\frac{1}{2} ln (x^{2} + y^{2}))

(d^2)/(dx^2)(1/((x-1)^2))

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

Frequently Asked Questions (FAQ)

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