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Popular >

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

Solution

derivative of

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

Solution

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

Apply the chain rule:

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

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

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

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

Simplify

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

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\frac{d}{d x} (x (3 x - 9)^{3})

integral from 0 to 5 of (2x-1)/(x+1)

\int_{0}^{5} \frac{2 x - 1}{x + 1} d x

integral from 0 to sqrt(2 of)xe^{-x^2}

\int_{0}^{2} x e^{- x^{2}} d x

integral of |x|

\int ∣ x ∣ d x

(\partial)/(\partial x)(a^x-b^x)

\frac{\partial}{\partial x} (a^{x} - b^{x})

Frequently Asked Questions (FAQ)

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