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Popular >

derivative of (2/(x-1)^5)

Solution

\frac{d}{d x} ((\frac{2}{x - 1})^{5})

Solution

- \frac{160}{( x - 1 ) ^{6}}

Solution steps

\frac{d}{d x} ((\frac{2}{x - 1})^{5})

Apply the chain rule:

5 (\frac{2}{x - 1})^{4} \frac{d}{d x} (\frac{2}{x - 1})

= 5 (\frac{2}{x - 1})^{4} \frac{d}{d x} (\frac{2}{x - 1})

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

= 5 (\frac{2}{x - 1})^{4} (- \frac{2}{( x - 1 ) ^{2}})

Simplify

5 (\frac{2}{x - 1})^{4} (- \frac{2}{( x - 1 ) ^{2}}) : - \frac{160}{( x - 1 ) ^{6}}

= - \frac{160}{( x - 1 ) ^{6}}

Popular Examples

derivative of 1/x-x

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

integral of sqrt(x)+2

\int x + 2 d x

derivative of f(t)=3tsin(pit)derivative of

f (t) = 3 t sin (π t)

integral of 3x*2^{x^2}

\int 3 x \cdot 2^{x^{2}} d x

limit as x approaches 0 of (sin(x))/(3x)

x \to 0 lim (\frac{sin ( x )}{3 x})

Frequently Asked Questions (FAQ)

What is the derivative of (2/(x-1)^5) ?
The derivative of (2/(x-1)^5) is -(160)/((x-1)^6)
What is the first derivative of (2/(x-1)^5) ?
The first derivative of (2/(x-1)^5) is -(160)/((x-1)^6)