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The derivative of the function/ sqrt(3x-2)

Derivative of sqrt(3x-2)

The solution

You have entered [src]

  _________
\/ 3*x - 2

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

sqrt(3*x - 2)

Detail solution

Let $u = 3 x - 2$ .
Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(3 x - 2\right)$ :
1. Differentiate $3 x - 2$ term by term:
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x$ goes to $1$
    So, the result is: $3$
  2. The derivative of the constant $-2$ is zero.
  The result is: $3$
The result of the chain rule is:

$\frac{3}{2 \sqrt{3 x - 2}}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

      -9       
---------------
            3/2
4*(-2 + 3*x)

$$- \frac{9}{4 \left(3 x - 2\right)^{\frac{3}{2}}}$$

Simplify

The third derivative [src]

       81      
---------------
            5/2
8*(-2 + 3*x)

$$\frac{81}{8 \left(3 x - 2\right)^{\frac{5}{2}}}$$

Simplify

The graph

Derivative of sqrt(3x-2)