Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of (1-x^2)^(1/2)
Derivative of x-5
Derivative of 2*sinh(x)*cosh(x)
Derivative of x*ln(x)
Identical expressions
((eight thousand + five hundred and seventy / two)/(five * zero . one hundred and twenty-five * zero . one hundred and ninety-five))*ln((ninety - twenty-nine)/(x- twenty-nine))
((8000 plus 570 divide by 2) divide by (5 multiply by 0.125 multiply by 0.195)) multiply by ln((90 minus 29) divide by (x minus 29))
((eight thousand plus five hundred and seventy divide by two) divide by (five multiply by zero . one hundred and twenty minus five multiply by zero . one hundred and ninety minus five)) multiply by ln((ninety minus twenty minus nine) divide by (x minus twenty minus nine))
((8000+570/2)/(50.1250.195))ln((90-29)/(x-29))
8000+570/2/50.1250.195ln90-29/x-29
((8000+570 divide by 2) divide by (5*0.125*0.195))*ln((90-29) divide by (x-29))
Similar expressions
((8000+570/2)/(5*0.125*0.195))*ln((90-29)/(x+29))
((8000-570/2)/(5*0.125*0.195))*ln((90-29)/(x-29))
((8000+570/2)/(5*0.125*0.195))*ln((90+29)/(x-29))

The derivative of the function/ ((8000+570/2)/(5*0.125*0.195))*ln((90-29)/(x-29))

Derivative of ((8000+570/2)/(50.1250.195))*ln((90-29)/(x-29))

The solution

You have entered [src]

285 + 8000    /  61  \
----------*log|------|
  /5   \      \x - 29/
  |-*39|              
  |8   |              
  |----|              
  \200 /

$$\frac{285 + 8000}{\frac{39}{200} \frac{5}{8}} \log{\left(\frac{61}{x - 29} \right)}$$

((285 + 8000)/(((5/8)*39/200)))*log(61/(x - 29))

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = \frac{61}{x - 29}$ .
2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \frac{61}{x - 29}$ :
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Let $u = x - 29$ .
    2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
    3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x - 29\right)$ :
      1. Differentiate $x - 29$ term by term:
        
        Apply the power rule: $x$ goes to $1$
        
        The derivative of the constant $-29$ is zero.
        
        The result is: $1$
      The result of the chain rule is:
      
      $- \frac{1}{\left(x - 29\right)^{2}}$
    So, the result is: $- \frac{61}{\left(x - 29\right)^{2}}$
  The result of the chain rule is:
  
  $- \frac{61 \left(\frac{x}{61} - \frac{29}{61}\right)}{\left(x - 29\right)^{2}}$
So, the result is: $- \frac{19520 \left(285 + 8000\right) \left(\frac{x}{61} - \frac{29}{61}\right)}{39 \left(x - 29\right)^{2}}$
Now simplify:

$- \frac{2651200}{39 x - 1131}$

The answer is:

$- \frac{2651200}{39 x - 1131}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

                    /  29   x \
-19520*(285 + 8000)*|- -- + --|
                    \  61   61/
-------------------------------
                     2         
          39*(x - 29)

$$- \frac{19520 \left(285 + 8000\right) \left(\frac{x}{61} - \frac{29}{61}\right)}{39 \left(x - 29\right)^{2}}$$

Simplify

The second derivative [src]

   2651200   
-------------
            2
39*(-29 + x)

$$\frac{2651200}{39 \left(x - 29\right)^{2}}$$

Simplify

The third derivative [src]

  -5302400   
-------------
            3
39*(-29 + x)

$$- \frac{5302400}{39 \left(x - 29\right)^{3}}$$

Simplify

Other calculators

How to use it?

Identical expressions

Similar expressions

Derivative of ((8000+570/2)/(50.1250.195))*ln((90-29)/(x-29))

The graph:

Piecewise:

The solution

Other calculators

How to use it?

Identical expressions

Similar expressions

Derivative of ((8000+570/2)/(5*0.125*0.195))*ln((90-29)/(x-29))

The graph:

Piecewise:

The solution

Derivative of ((8000+570/2)/(50.1250.195))*ln((90-29)/(x-29))