What is the derivative of xsqrt(x-1) ?

The derivative of xsqrt(x-1) is (3x-2)/(2sqrt(x-1))

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

The first derivative of xsqrt(x-1) is (3x-2)/(2sqrt(x-1))

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

\frac{3 x - 2}{2 x - 1}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = x - 1

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

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

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

= 1 \cdot x - 1 + \frac{1}{2 x - 1} x

Simplify

1 \cdot x - 1 + \frac{1}{2 x - 1} x : \frac{3 x - 2}{2 x - 1}

= \frac{3 x - 2}{2 x - 1}

What is the derivative of xsqrt(x-1) ?
The derivative of xsqrt(x-1) is (3x-2)/(2sqrt(x-1))
What is the first derivative of xsqrt(x-1) ?
The first derivative of xsqrt(x-1) is (3x-2)/(2sqrt(x-1))