Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of (x^2+1)^3
Derivative of (x+3)/(x-2)
Derivative of x^2*asinh(x)*acosh(x)
Derivative of (x-2)^2*(x-4)+5
Identical expressions
y=ln^ two (3x- two)
y equally ln squared (3x minus 2)
y equally ln to the power of two (3x minus two)
y=ln2(3x-2)
y=ln23x-2
y=ln²(3x-2)
y=ln to the power of 2(3x-2)
y=ln^23x-2
Similar expressions
y=ln^2(3x+2)

The derivative of the function/ y=ln^2(3x-2)

Derivative of y=ln^2(3x-2)

The solution

You have entered [src]

   2         
log (3*x - 2)

$$\log{\left(3 x - 2 \right)}^{2}$$

d /   2         \
--\log (3*x - 2)/
dx

$$\frac{d}{d x} \log{\left(3 x - 2 \right)}^{2}$$

Transform

Detail solution

Let $u = \log{\left(3 x - 2 \right)}$ .
Apply the power rule: $u^{2}$ goes to $2 u$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \log{\left(3 x - 2 \right)}$ :
1. Let $u = 3 x - 2$ .
2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
3. 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 $\left(-1\right) 2$ is zero.
    The result is: $3$
  The result of the chain rule is:
  
  $\frac{3}{3 x - 2}$
The result of the chain rule is:

$\frac{6 \log{\left(3 x - 2 \right)}}{3 x - 2}$
Now simplify:

$\frac{6 \log{\left(3 x - 2 \right)}}{3 x - 2}$

The answer is:

$\frac{6 \log{\left(3 x - 2 \right)}}{3 x - 2}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

6*log(3*x - 2)
--------------
   3*x - 2

$$\frac{6 \log{\left(3 x - 2 \right)}}{3 x - 2}$$

Simplify

The second derivative [src]

18*(1 - log(-2 + 3*x))
----------------------
               2      
     (-2 + 3*x)

$$\frac{18 \cdot \left(- \log{\left(3 x - 2 \right)} + 1\right)}{\left(3 x - 2\right)^{2}}$$

Simplify

The third derivative [src]

54*(-3 + 2*log(-2 + 3*x))
-------------------------
                 3       
       (-2 + 3*x)

$$\frac{54 \cdot \left(2 \log{\left(3 x - 2 \right)} - 3\right)}{\left(3 x - 2\right)^{3}}$$

Simplify

The graph

Derivative of y=ln^2(3x-2)