What is the derivative of xsqrt(x-3) ?

The derivative of xsqrt(x-3) is (3x-6)/(2sqrt(x-3))

What is the first derivative of xsqrt(x-3) ?

The first derivative of xsqrt(x-3) is (3x-6)/(2sqrt(x-3))

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

\frac{3 x - 6}{2 x - 3}

Solution steps

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

Apply the Product Rule:

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

f = x, g = x - 3

= \frac{d x}{d x} x - 3 + \frac{d}{d x} (x - 3) x

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

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

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

Simplify

1 \cdot x - 3 + \frac{1}{2 x - 3} x : \frac{3 x - 6}{2 x - 3}

= \frac{3 x - 6}{2 x - 3}

What is the derivative of xsqrt(x-3) ?
The derivative of xsqrt(x-3) is (3x-6)/(2sqrt(x-3))
What is the first derivative of xsqrt(x-3) ?
The first derivative of xsqrt(x-3) is (3x-6)/(2sqrt(x-3))