Derivative of 3sqrtx

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3*\/ x

$$3 \sqrt{x}$$

3*sqrt(x)

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Apply the power rule: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$
So, the result is: $\frac{3}{2 \sqrt{x}}$

The answer is:

$\frac{3}{2 \sqrt{x}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   3   
-------
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2*\/ x

$$\frac{3}{2 \sqrt{x}}$$

Simplify

The second derivative [src]

 -3   
------
   3/2
4*x

$$- \frac{3}{4 x^{\frac{3}{2}}}$$

Simplify

The third derivative [src]

  9   
------
   5/2
8*x

$$\frac{9}{8 x^{\frac{5}{2}}}$$

Simplify

The graph