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Popular >

derivative of f(x)= x/(x-1)

Solution

derivative of

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

Solution

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

Solution steps

\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

tangent of f(x)=3-5x+2x^2,(-9,210)tangent of

f (x) = 3 - 5 x + 2 x^{2}, (- 9, 210)

(x+y)^2dx+(2xy+x^2-9)dy=0

(x + y)^{2} d x + (2 x y + x^{2} - 9) d y = 0

limit as x approaches infinity of x/(2x)

x \to \infty lim (\frac{x}{2 x})

(\partial)/(\partial x)(x/(2+y))

\frac{\partial}{\partial x} (\frac{x}{2 + y})

f(t)=cos(ln(t))

f (t) = cos (ln (t))

Frequently Asked Questions (FAQ)

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