What is the derivative of 6/(x-1) ?

The derivative of 6/(x-1) is -6/((x-1)^2)

What is the first derivative of 6/(x-1) ?

The first derivative of 6/(x-1) is -6/((x-1)^2)

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\frac{d}{d x} (\frac{6}{x - 1})

- \frac{6}{( x - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{6}{x - 1})

Take the constant out:

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

= 6 \frac{d}{d x} (\frac{1}{x - 1})

Apply exponent rule:

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

= 6 \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

= 6 (- \frac{1}{( x - 1 ) ^{2}} \cdot 1)

Simplify

6 (- \frac{1}{( x - 1 ) ^{2}} \cdot 1) : - \frac{6}{( x - 1 ) ^{2}}

= - \frac{6}{( x - 1 ) ^{2}}

\int_{0}^{1} 3 - x^{2} d x

\frac{d y}{d t} - 26 t^{12} e^{- y} = 0

\frac{2}{( x + 1 ) ^{3}}

f (x) = \frac{4 x}{x ^{2} + 1}, (1, 2)

4 e^{\frac{t}{2}}

What is the derivative of 6/(x-1) ?
The derivative of 6/(x-1) is -6/((x-1)^2)
What is the first derivative of 6/(x-1) ?
The first derivative of 6/(x-1) is -6/((x-1)^2)