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Derivative of y=4*log2(x)+8*x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
  log(x)      
4*------ + 8*x
  log(2)      
$$8 x + 4 \frac{\log{\left(x \right)}}{\log{\left(2 \right)}}$$
4*(log(x)/log(2)) + 8*x
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 a constant times a function is the constant times the derivative of the function.

        1. The derivative of is .

        So, the result is:

      So, the result is:

    2. 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:

    The result is:


The answer is:

The graph
The first derivative [src]
       4    
8 + --------
    x*log(2)
$$8 + \frac{4}{x \log{\left(2 \right)}}$$
The second derivative [src]
   -4    
---------
 2       
x *log(2)
$$- \frac{4}{x^{2} \log{\left(2 \right)}}$$
The third derivative [src]
    8    
---------
 3       
x *log(2)
$$\frac{8}{x^{3} \log{\left(2 \right)}}$$