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Derivative of log(6^sqrt(x))

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   /   ___\
   | \/ x |
log\6     /
$$\log{\left(6^{\sqrt{x}} \right)}$$
log(6^(sqrt(x)))
Detail solution
  1. Let .

  2. The derivative of is .

  3. Then, apply the chain rule. Multiply by :

    1. Let .

    2. Then, apply the chain rule. Multiply by :

      1. Apply the power rule: goes to

      The result of the chain rule is:

    The result of the chain rule is:


The answer is:

The graph
The first derivative [src]
 log(6)
-------
    ___
2*\/ x 
$$\frac{\log{\left(6 \right)}}{2 \sqrt{x}}$$
The second derivative [src]
-log(6) 
--------
    3/2 
 4*x    
$$- \frac{\log{\left(6 \right)}}{4 x^{\frac{3}{2}}}$$
The third derivative [src]
3*log(6)
--------
    5/2 
 8*x    
$$\frac{3 \log{\left(6 \right)}}{8 x^{\frac{5}{2}}}$$