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

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

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

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

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derivative of

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

\frac{x - 1}{2 x}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

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

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

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

Simplify

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

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

2 x^{2} - 5 x + 3, at x = 0

x^{t a n (x)}

\frac{d y}{d x} = cos (y - x)

\int_{0}^{N} e^{- s t} sin (5 t) d t

\frac{1}{s ( 2 s + 1 )}

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