What is the derivative of sqrt(x)dx ?

The derivative of sqrt(x)dx is (3dsqrt(x))/2

What is the first derivative of sqrt(x)dx ?

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

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

\frac{3 d x}{2}

Solution steps

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

Treat

d

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = x

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

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

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

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

Simplify

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

= \frac{3 d x}{2}

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