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Derivative of sqrt(x)*log(x,2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
  ___ log(x)
\/ x *------
      log(2)
$$\sqrt{x} \frac{\log{\left(x \right)}}{\log{\left(2 \right)}}$$
sqrt(x)*(log(x)/log(2))
Detail solution
  1. Apply the quotient rule, which is:

    and .

    To find :

    1. Apply the product rule:

      ; to find :

      1. Apply the power rule: goes to

      ; to find :

      1. The derivative of is .

      The result is:

    To find :

    1. The derivative of the constant is zero.

    Now plug in to the quotient rule:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
     1             log(x)    
------------ + --------------
  ___              ___       
\/ x *log(2)   2*\/ x *log(2)
$$\frac{\log{\left(x \right)}}{2 \sqrt{x} \log{\left(2 \right)}} + \frac{1}{\sqrt{x} \log{\left(2 \right)}}$$
The second derivative [src]
   -log(x)   
-------------
   3/2       
4*x   *log(2)
$$- \frac{\log{\left(x \right)}}{4 x^{\frac{3}{2}} \log{\left(2 \right)}}$$
The third derivative [src]
-2 + 3*log(x)
-------------
   5/2       
8*x   *log(2)
$$\frac{3 \log{\left(x \right)} - 2}{8 x^{\frac{5}{2}} \log{\left(2 \right)}}$$