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The derivative of the function/ ln(10x-3)^4

Derivative of ln(10x-3)^4

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   4          
log (10*x - 3)
$$\log{\left(10 x - 3 \right)}^{4}$$ 
log(10*x - 3)^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. 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:

  4. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      3          
40*log (10*x - 3)
-----------------
     10*x - 3
$$\frac{40 \log{\left(10 x - 3 \right)}^{3}}{10 x - 3}$$
Simplify
The second derivative [src] 
       2                                
400*log (-3 + 10*x)*(3 - log(-3 + 10*x))
----------------------------------------
                         2              
              (-3 + 10*x)
$$\frac{400 \left(3 - \log{\left(10 x - 3 \right)}\right) \log{\left(10 x - 3 \right)}^{2}}{\left(10 x - 3\right)^{2}}$$
Simplify
The third derivative [src] 
     /                            2           \               
4000*\6 - 9*log(-3 + 10*x) + 2*log (-3 + 10*x)/*log(-3 + 10*x)
--------------------------------------------------------------
                                    3                         
                         (-3 + 10*x)
$$\frac{4000 \left(2 \log{\left(10 x - 3 \right)}^{2} - 9 \log{\left(10 x - 3 \right)} + 6\right) \log{\left(10 x - 3 \right)}}{\left(10 x - 3\right)^{3}}$$
Simplify
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