Mister Exam

Derivative of y=log(tan4-3x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
log(tan(4) - 3*x)
log(3x+tan(4))\log{\left(- 3 x + \tan{\left(4 \right)} \right)}
d                    
--(log(tan(4) - 3*x))
dx                   
ddxlog(3x+tan(4))\frac{d}{d x} \log{\left(- 3 x + \tan{\left(4 \right)} \right)}
Detail solution
  1. Let u=3x+tan(4)u = - 3 x + \tan{\left(4 \right)}.

  2. The derivative of log(u)\log{\left(u \right)} is 1u\frac{1}{u}.

  3. Then, apply the chain rule. Multiply by ddx(3x+tan(4))\frac{d}{d x} \left(- 3 x + \tan{\left(4 \right)}\right):

    1. Differentiate 3x+tan(4)- 3 x + \tan{\left(4 \right)} term by term:

      1. Rewrite the function to be differentiated:

        tan(4)=sin(4)cos(4)\tan{\left(4 \right)} = \frac{\sin{\left(4 \right)}}{\cos{\left(4 \right)}}

      2. The derivative of the constant sin(4)cos(4)\frac{\sin{\left(4 \right)}}{\cos{\left(4 \right)}} is zero.

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

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

          1. Apply the power rule: xx goes to 11

          So, the result is: 33

        So, the result is: 3-3

      The result is: 3-3

    The result of the chain rule is:

    33x+tan(4)- \frac{3}{- 3 x + \tan{\left(4 \right)}}

  4. Now simplify:

    33xtan(4)\frac{3}{3 x - \tan{\left(4 \right)}}


The answer is:

33xtan(4)\frac{3}{3 x - \tan{\left(4 \right)}}

The graph
02468-8-6-4-2-1010-2020
The first derivative [src]
    -3      
------------
tan(4) - 3*x
33x+tan(4)- \frac{3}{- 3 x + \tan{\left(4 \right)}}
The second derivative [src]
      -9        
----------------
               2
(-tan(4) + 3*x) 
9(3xtan(4))2- \frac{9}{\left(3 x - \tan{\left(4 \right)}\right)^{2}}
The third derivative [src]
       54       
----------------
               3
(-tan(4) + 3*x) 
54(3xtan(4))3\frac{54}{\left(3 x - \tan{\left(4 \right)}\right)^{3}}
The graph
Derivative of y=log(tan4-3x)