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y=ln(10x^ three -x^ two)
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y=ln10x^3-x^2
Similar expressions
y=ln(10x^3+x^2)

The derivative of the function/ y=ln(10x^3-x^2)

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

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

Let $u = 10 x^{3} - x^{2}$ .
The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(10 x^{3} - x^{2}\right)$ :
1. Differentiate $10 x^{3} - x^{2}$ 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: $x^{3}$ goes to $3 x^{2}$
    So, the result is: $30 x^{2}$
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x^{2}$ goes to $2 x$
    So, the result is: $- 2 x$
  The result is: $30 x^{2} - 2 x$
The result of the chain rule is:

$\frac{30 x^{2} - 2 x}{10 x^{3} - x^{2}}$
Now simplify:

$\frac{2 \left(15 x - 1\right)}{x \left(10 x - 1\right)}$

The answer is:

$\frac{2 \left(15 x - 1\right)}{x \left(10 x - 1\right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

           2
-2*x + 30*x 
------------
     3    2 
 10*x  - x

$$\frac{30 x^{2} - 2 x}{10 x^{3} - x^{2}}$$

Simplify

The second derivative [src]

  /                         2\
  |            2*(-1 + 15*x) |
2*|-1 + 30*x - --------------|
  \              -1 + 10*x   /
------------------------------
         2                    
        x *(-1 + 10*x)

$$\frac{2 \left(30 x - 1 - \frac{2 \left(15 x - 1\right)^{2}}{10 x - 1}\right)}{x^{2} \left(10 x - 1\right)}$$

Simplify

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)

$$\frac{4 \left(15 - \frac{3 \left(15 x - 1\right) \left(30 x - 1\right)}{x \left(10 x - 1\right)} + \frac{4 \left(15 x - 1\right)^{3}}{x \left(10 x - 1\right)^{2}}\right)}{x^{2} \left(10 x - 1\right)}$$

Simplify

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)

Simplify

The graph

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

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