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Derivative of ln^4*(sqrt(3*x+5))

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
   4/  _________\
log \\/ 3*x + 5 /
$$\log{\left(\sqrt{3 x + 5} \right)}^{4}$$
log(sqrt(3*x + 5))^4
Detail solution
  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    1. Let .

    2. The derivative of is .

    3. Then, apply the chain rule. Multiply by :

      1. Let .

      2. Apply the power rule: goes to

      3. Then, apply the chain rule. Multiply by :

        1. Differentiate 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: goes to

            So, the result is:

          2. The derivative of the constant is zero.

          The result is:

        The result of the chain rule is:

      The result of the chain rule is:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
     3/  _________\
6*log \\/ 3*x + 5 /
-------------------
      3*x + 5      
$$\frac{6 \log{\left(\sqrt{3 x + 5} \right)}^{3}}{3 x + 5}$$
The second derivative [src]
     2/  _________\ /         /  _________\\
9*log \\/ 5 + 3*x /*\3 - 2*log\\/ 5 + 3*x //
--------------------------------------------
                          2                 
                 (5 + 3*x)                  
$$\frac{9 \left(3 - 2 \log{\left(\sqrt{3 x + 5} \right)}\right) \log{\left(\sqrt{3 x + 5} \right)}^{2}}{\left(3 x + 5\right)^{2}}$$
The third derivative [src]
   /         /  _________\        2/  _________\\    /  _________\
27*\3 - 9*log\\/ 5 + 3*x / + 4*log \\/ 5 + 3*x //*log\\/ 5 + 3*x /
------------------------------------------------------------------
                                     3                            
                            (5 + 3*x)                             
$$\frac{27 \left(4 \log{\left(\sqrt{3 x + 5} \right)}^{2} - 9 \log{\left(\sqrt{3 x + 5} \right)} + 3\right) \log{\left(\sqrt{3 x + 5} \right)}}{\left(3 x + 5\right)^{3}}$$