Mister Exam

Derivative of 3/x^5

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
3 
--
 5
x 
3x5\frac{3}{x^{5}}
3/x^5
Detail solution
  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Let u=x5u = x^{5}.

    2. Apply the power rule: 1u\frac{1}{u} goes to 1u2- \frac{1}{u^{2}}

    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:

      5x6- \frac{5}{x^{6}}

    So, the result is: 15x6- \frac{15}{x^{6}}


The answer is:

15x6- \frac{15}{x^{6}}

The graph
02468-8-6-4-2-1010-2000000020000000
The first derivative [src]
-15 
----
  6 
 x  
15x6- \frac{15}{x^{6}}
The second derivative [src]
90
--
 7
x 
90x7\frac{90}{x^{7}}
The third derivative [src]
-630 
-----
   8 
  x  
630x8- \frac{630}{x^{8}}
The graph
Derivative of 3/x^5