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log3(x)+logx(3)
The derivative of the function/ log3(x)+logx(3)

Derivative of log3(x)+logx(3)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
log(x)           
------ + log(x)*3
log(3)
$$\frac{\log{\left(x \right)}}{\log{\left(3 \right)}} + 3 \log{\left(x \right)}$$ 
log(x)/log(3) + log(x)*3
Detail solution

  1. Differentiate term by term:

    1. 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:

    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:

  2. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
3      1    
- + --------
x   x*log(3)
$$\frac{1}{x \log{\left(3 \right)}} + \frac{3}{x}$$
Simplify
The second derivative [src] 
 /      1   \ 
-|3 + ------| 
 \    log(3)/ 
--------------
       2      
      x
$$- \frac{\frac{1}{\log{\left(3 \right)}} + 3}{x^{2}}$$
Simplify
The third derivative [src] 
  /      1   \
2*|3 + ------|
  \    log(3)/
--------------
       3      
      x
$$\frac{2 \left(\frac{1}{\log{\left(3 \right)}} + 3\right)}{x^{3}}$$
Simplify
The graph
Derivative of log3(x)+logx(3)
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