What is the derivative of sqrt(x)(3x-1) ?

The derivative of sqrt(x)(3x-1) is (9x-1)/(2sqrt(x))

What is the first derivative of sqrt(x)(3x-1) ?

The first derivative of sqrt(x)(3x-1) is (9x-1)/(2sqrt(x))

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derivative of

x (3 x - 1)

\frac{9 x - 1}{2 x}

Solution steps

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

Apply the Product Rule:

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

f = x, g = 3 x - 1

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

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

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

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

Simplify

\frac{1}{2 x} (3 x - 1) + 3 x : \frac{9 x - 1}{2 x}

= \frac{9 x - 1}{2 x}

What is the derivative of sqrt(x)(3x-1) ?
The derivative of sqrt(x)(3x-1) is (9x-1)/(2sqrt(x))
What is the first derivative of sqrt(x)(3x-1) ?
The first derivative of sqrt(x)(3x-1) is (9x-1)/(2sqrt(x))