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}

\int \frac{ln ( z )}{z ^{2}} d z

\int_{- 1}^{3} \frac{4 x ^{2} - 7}{2 x + 3} d x

\frac{d}{d x} (I n)

\frac{d y}{d x} = 12 x^{3} y

\int (e^{x} + 1) (e^{x} + x) d 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))