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Popular >

derivative of 1/((x-1))

Solution

derivative of

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

Popular Examples

integral of (x^2+2x)e^{x^3+3x^2-1}

\int (x^{2} + 2 x) e^{x^{3} + 3 x^{2} - 1} d x

tangent of f(x)=(x-1)^2+1,\at x=-1 tangent of

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

area f(x)=-10x+5,(1,2)area

f (x) = - 10 x + 5, (1, 2)

integral of x^2sqrt(4x^2+1)

\int x^{2} 4 x^{2} + 1 d x

limit as x approaches 3 of (x^2)/x

x \to 3 lim (\frac{x ^{2}}{x})

Frequently Asked Questions (FAQ)

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