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е^(-lnx^3)^5

Derivative of е^(-lnx^3)^5

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
 /          5\
 |/    3   \ |
 \\-log (x)/ /
e             
$$e^{\left(- \log{\left(x \right)}^{3}\right)^{5}}$$
  / /          5\\
  | |/    3   \ ||
d | \\-log (x)/ /|
--\e             /
dx                
$$\frac{d}{d x} e^{\left(- \log{\left(x \right)}^{3}\right)^{5}}$$
Detail solution
  1. Let .

  2. The derivative of is itself.

  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. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Let .

        2. Apply the power rule: goes to

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

          1. The derivative of is .

          The result of the chain rule is:

        So, 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
The first derivative [src]
              /          5\
              |/    3   \ |
       14     \\-log (x)/ /
-15*log  (x)*e             
---------------------------
             x             
$$- \frac{15 e^{\left(- \log{\left(x \right)}^{3}\right)^{5}} \log{\left(x \right)}^{14}}{x}$$
The second derivative [src]
                                          /          5\
                                          |/    3   \ |
      13    /            15            \  \\-log (x)/ /
15*log  (x)*\-14 + 15*log  (x) + log(x)/*e             
-------------------------------------------------------
                            2                          
                           x                           
$$\frac{15 \cdot \left(15 \log{\left(x \right)}^{15} + \log{\left(x \right)} - 14\right) e^{\left(- \log{\left(x \right)}^{3}\right)^{5}} \log{\left(x \right)}^{13}}{x^{2}}$$
The third derivative [src]
                                                                                        /          5\
                                                                                        |/    3   \ |
      12    /              30            16           2                         15   \  \\-log (x)/ /
15*log  (x)*\-182 - 225*log  (x) - 45*log  (x) - 2*log (x) + 42*log(x) + 630*log  (x)/*e             
-----------------------------------------------------------------------------------------------------
                                                   3                                                 
                                                  x                                                  
$$\frac{15 \left(- 225 \log{\left(x \right)}^{30} - 45 \log{\left(x \right)}^{16} + 630 \log{\left(x \right)}^{15} - 2 \log{\left(x \right)}^{2} + 42 \log{\left(x \right)} - 182\right) e^{\left(- \log{\left(x \right)}^{3}\right)^{5}} \log{\left(x \right)}^{12}}{x^{3}}$$
The graph
Derivative of е^(-lnx^3)^5