What is the derivative of f(x)= 2/((x-1)^3) ?

The derivative of f(x)= 2/((x-1)^3) is -6/((x-1)^4)

What is the first derivative of f(x)= 2/((x-1)^3) ?

The first derivative of f(x)= 2/((x-1)^3) is -6/((x-1)^4)

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derivative of

f (x) = \frac{2}{( x - 1 ) ^{3}}

- \frac{6}{( x - 1 ) ^{4}}

Solution steps

\frac{d}{d x} (\frac{2}{( x - 1 ) ^{3}})

Take the constant out:

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

= 2 \frac{d}{d x} (\frac{1}{( x - 1 ) ^{3}})

Apply exponent rule:

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

= 2 \frac{d}{d x} ((x - 1)^{- 3})

Apply the chain rule:

- \frac{3}{( x - 1 ) ^{4}} \frac{d}{d x} (x - 1)

= - \frac{3}{( x - 1 ) ^{4}} \frac{d}{d x} (x - 1)

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

= 2 (- \frac{3}{( x - 1 ) ^{4}} \cdot 1)

Simplify

2 (- \frac{3}{( x - 1 ) ^{4}} \cdot 1) : - \frac{6}{( x - 1 ) ^{4}}

= - \frac{6}{( x - 1 ) ^{4}}

\int \frac{1}{x ( x + x )} d x

\int (3 x - 1) (x + 1) d x

\int \frac{sin ( 3 x )}{2 + cos ( 3 x )} d x

\int a r cos (x) d x

y = x \frac{a ^{2} - x ^{2}}{x}

What is the derivative of f(x)= 2/((x-1)^3) ?
The derivative of f(x)= 2/((x-1)^3) is -6/((x-1)^4)
What is the first derivative of f(x)= 2/((x-1)^3) ?
The first derivative of f(x)= 2/((x-1)^3) is -6/((x-1)^4)