Mister Exam

Other calculators

The derivative of the function/ sin(1-log10(x))

Derivative of sin(1-log10(x))

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   /     log(x)\
sin|1 - -------|
   \    log(10)/
$$\sin{\left(- \frac{\log{\left(x \right)}}{\log{\left(10 \right)}} + 1 \right)}$$ 
sin(1 - log(x)/log(10))
Detail solution

  1. Let .

  2. The derivative of sine is cosine:

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

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

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

        1. The derivative of is .

        So, the result is:

      The result 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] 
    /      log(x)\ 
-cos|-1 + -------| 
    \     log(10)/ 
-------------------
     x*log(10)
$$- \frac{\cos{\left(\frac{\log{\left(x \right)}}{\log{\left(10 \right)}} - 1 \right)}}{x \log{\left(10 \right)}}$$
Simplify
The second derivative [src] 
   /      log(x)\                    
sin|-1 + -------|                    
   \     log(10)/      /      log(x)\
----------------- + cos|-1 + -------|
     log(10)           \     log(10)/
-------------------------------------
               2                     
              x *log(10)
$$\frac{\frac{\sin{\left(\frac{\log{\left(x \right)}}{\log{\left(10 \right)}} - 1 \right)}}{\log{\left(10 \right)}} + \cos{\left(\frac{\log{\left(x \right)}}{\log{\left(10 \right)}} - 1 \right)}}{x^{2} \log{\left(10 \right)}}$$
Simplify
The third derivative [src] 
                           /      log(x)\        /      log(x)\
                        cos|-1 + -------|   3*sin|-1 + -------|
       /      log(x)\      \     log(10)/        \     log(10)/
- 2*cos|-1 + -------| + ----------------- - -------------------
       \     log(10)/           2                 log(10)      
                             log (10)                          
---------------------------------------------------------------
                            3                                  
                           x *log(10)
$$\frac{- \frac{3 \sin{\left(\frac{\log{\left(x \right)}}{\log{\left(10 \right)}} - 1 \right)}}{\log{\left(10 \right)}} - 2 \cos{\left(\frac{\log{\left(x \right)}}{\log{\left(10 \right)}} - 1 \right)} + \frac{\cos{\left(\frac{\log{\left(x \right)}}{\log{\left(10 \right)}} - 1 \right)}}{\log{\left(10 \right)}^{2}}}{x^{3} \log{\left(10 \right)}}$$
Simplify
    © Mister Exam – Calculator