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y=ln(10x^3-x^2)

Derivative of y=ln(10x^3-x^2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   /    3    2\
log\10*x  - x /
$$\log{\left(10 x^{3} - x^{2} \right)}$$
log(10*x^3 - x^2)
Detail solution
  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 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:

      The result is:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
           2
-2*x + 30*x 
------------
     3    2 
 10*x  - x  
$$\frac{30 x^{2} - 2 x}{10 x^{3} - x^{2}}$$
The second derivative [src]
  /                         2\
  |            2*(-1 + 15*x) |
2*|-1 + 30*x - --------------|
  \              -1 + 10*x   /
------------------------------
         2                    
        x *(-1 + 10*x)        
$$\frac{2 \left(30 x - 1 - \frac{2 \left(15 x - 1\right)^{2}}{10 x - 1}\right)}{x^{2} \left(10 x - 1\right)}$$
The third derivative [src]
  /                  3                            \
  |     4*(-1 + 15*x)    3*(-1 + 15*x)*(-1 + 30*x)|
4*|15 + -------------- - -------------------------|
  |                  2         x*(-1 + 10*x)      |
  \     x*(-1 + 10*x)                             /
---------------------------------------------------
                    2                              
                   x *(-1 + 10*x)                  
$$\frac{4 \left(15 - \frac{3 \left(15 x - 1\right) \left(30 x - 1\right)}{x \left(10 x - 1\right)} + \frac{4 \left(15 x - 1\right)^{3}}{x \left(10 x - 1\right)^{2}}\right)}{x^{2} \left(10 x - 1\right)}$$
3-я производная [src]
  /                  3                            \
  |     4*(-1 + 15*x)    3*(-1 + 15*x)*(-1 + 30*x)|
4*|15 + -------------- - -------------------------|
  |                  2         x*(-1 + 10*x)      |
  \     x*(-1 + 10*x)                             /
---------------------------------------------------
                    2                              
                   x *(-1 + 10*x)                  
$$\frac{4 \left(15 - \frac{3 \left(15 x - 1\right) \left(30 x - 1\right)}{x \left(10 x - 1\right)} + \frac{4 \left(15 x - 1\right)^{3}}{x \left(10 x - 1\right)^{2}}\right)}{x^{2} \left(10 x - 1\right)}$$
The graph
Derivative of y=ln(10x^3-x^2)