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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

f = x - 3, g = x

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

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

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

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

Simplify

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

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

x \to + 0 lim (\frac{14}{tan ( x )})

\int 3 x^{2} - 5 x - 7 d x

\frac{d}{d x} (sin (n arcsin (x)))

- 2 x

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