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Derivative of log(3x-5)+6^5

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

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The solution

You have entered [src]
log(3*x - 5) + 7776
$$\log{\left(3 x - 5 \right)} + 7776$$
log(3*x - 5) + 7776
Detail solution
  1. Differentiate term by term:

    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 the constant is zero.

        The result is:

      The result of the chain rule is:

    4. The derivative of the constant is zero.

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
   3   
-------
3*x - 5
$$\frac{3}{3 x - 5}$$
The second derivative [src]
    -9     
-----------
          2
(-5 + 3*x) 
$$- \frac{9}{\left(3 x - 5\right)^{2}}$$
The third derivative [src]
     54    
-----------
          3
(-5 + 3*x) 
$$\frac{54}{\left(3 x - 5\right)^{3}}$$