What is the derivative of f(x)= x/(sqrt(x-1)) ?

The derivative of f(x)= x/(sqrt(x-1)) is (x-2)/(2(x-1)sqrt(x-1))

What is the first derivative of f(x)= x/(sqrt(x-1)) ?

The first derivative of f(x)= x/(sqrt(x-1)) is (x-2)/(2(x-1)sqrt(x-1))

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

f (x) = 6^{x}

\int \frac{1}{x ^{2} 25 + x ^{2}} d x

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

5 t^{3}

(4, 1), (6, 7)

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