Mister Exam

Derivative of sqrt(x^5)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   ____
  /  5 
\/  x  
x5\sqrt{x^{5}}
sqrt(x^5)
Detail solution
  1. Let u=x5u = x^{5}.

  2. Apply the power rule: u\sqrt{u} goes to 12u\frac{1}{2 \sqrt{u}}

  3. Then, apply the chain rule. Multiply by ddxx5\frac{d}{d x} x^{5}:

    1. Apply the power rule: x5x^{5} goes to 5x45 x^{4}

    The result of the chain rule is:

    5x42x5\frac{5 x^{4}}{2 \sqrt{x^{5}}}


The answer is:

5x42x5\frac{5 x^{4}}{2 \sqrt{x^{5}}}

The graph
02468-8-6-4-2-10100500
The first derivative [src]
     ____
    /  5 
5*\/  x  
---------
   2*x   
5x52x\frac{5 \sqrt{x^{5}}}{2 x}
The second derivative [src]
      ____
     /  5 
15*\/  x  
----------
      2   
   4*x    
15x54x2\frac{15 \sqrt{x^{5}}}{4 x^{2}}
The third derivative [src]
      ____
     /  5 
15*\/  x  
----------
      3   
   8*x    
15x58x3\frac{15 \sqrt{x^{5}}}{8 x^{3}}
The graph
Derivative of sqrt(x^5)