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Derivative of:
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Derivative of 3/x^5
Identical expressions
ln(3x+ five)^ two
ln(3x plus 5) squared
ln(3x plus five) to the power of two
ln(3x+5)2
ln3x+52
ln(3x+5)²
ln(3x+5) to the power of 2
ln3x+5^2
Similar expressions
ln(3x-5)^2

The derivative of the function/ ln(3x+5)^2

Derivative of ln(3x+5)^2

The solution

You have entered [src]

   2         
log (3*x + 5)

$$\log{\left(3 x + 5 \right)}^{2}$$

Transform

Detail solution

Let $u = \log{\left(3 x + 5 \right)}$ .
Apply the power rule: $u^{2}$ goes to $2 u$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \log{\left(3 x + 5 \right)}$ :
1. Let $u = 3 x + 5$ .
2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(3 x + 5\right)$ :
  1. Differentiate $3 x + 5$ 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 $5$ is zero.
    The result is: $3$
  The result of the chain rule is:
  
  $\frac{3}{3 x + 5}$
The result of the chain rule is:

$\frac{6 \log{\left(3 x + 5 \right)}}{3 x + 5}$
Now simplify:

$\frac{6 \log{\left(3 x + 5 \right)}}{3 x + 5}$

The answer is:

$\frac{6 \log{\left(3 x + 5 \right)}}{3 x + 5}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

6*log(3*x + 5)
--------------
   3*x + 5

$$\frac{6 \log{\left(3 x + 5 \right)}}{3 x + 5}$$

Simplify

The second derivative [src]

18*(1 - log(5 + 3*x))
---------------------
               2     
      (5 + 3*x)

$$\frac{18 \left(1 - \log{\left(3 x + 5 \right)}\right)}{\left(3 x + 5\right)^{2}}$$

Simplify

The third derivative [src]

54*(-3 + 2*log(5 + 3*x))
------------------------
                3       
       (5 + 3*x)

$$\frac{54 \left(2 \log{\left(3 x + 5 \right)} - 3\right)}{\left(3 x + 5\right)^{3}}$$

Simplify

The graph

Derivative of ln(3x+5)^2