Mister Exam

Other calculators

The derivative of the function/ sqrt(x^5-7)

Derivative of sqrt(x^5-7)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   ________
  /  5     
\/  x  - 7
x5−7\sqrt{x^{5} - 7} 
  /   ________\
d |  /  5     |
--\\/  x  - 7 /
dx
ddxx5−7\frac{d}{d x} \sqrt{x^{5} - 7}
Transform
Detail solution

  1. Let u=x5−7u = x^{5} - 7.

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

  3. Then, apply the chain rule. Multiply by ddx(x5−7)\frac{d}{d x} \left(x^{5} - 7\right):

    1. Differentiate x5−7x^{5} - 7 term by term:

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

      2. The derivative of the constant (−1)7\left(-1\right) 7 is zero.

      The result is: 5x45 x^{4}

    The result of the chain rule is:

    5x42x5−7\frac{5 x^{4}}{2 \sqrt{x^{5} - 7}}

  4. Now simplify:

    5x42x5−7\frac{5 x^{4}}{2 \sqrt{x^{5} - 7}}

The answer is:

5x42x5−7\frac{5 x^{4}}{2 \sqrt{x^{5} - 7}}

The first derivative [src] 
        4    
     5*x     
-------------
     ________
    /  5     
2*\/  x  - 7
5x42x5−7\frac{5 x^{4}}{2 \sqrt{x^{5} - 7}}
Simplify
The second derivative [src] 
     /           5   \
   3 |        5*x    |
5*x *|2 - -----------|
     |      /      5\|
     \    4*\-7 + x //
----------------------
        _________     
       /       5      
     \/  -7 + x
5x3(−5x54(x5−7)+2)x5−7\frac{5 x^{3} \left(- \frac{5 x^{5}}{4 \left(x^{5} - 7\right)} + 2\right)}{\sqrt{x^{5} - 7}}
Simplify
The third derivative [src] 
      /         5           10   \
    2 |      5*x        25*x     |
15*x *|2 - ------- + ------------|
      |          5              2|
      |    -7 + x      /      5\ |
      \              8*\-7 + x / /
----------------------------------
              _________           
             /       5            
           \/  -7 + x
15x2⋅(25x108(x5−7)2−5x5x5−7+2)x5−7\frac{15 x^{2} \cdot \left(\frac{25 x^{10}}{8 \left(x^{5} - 7\right)^{2}} - \frac{5 x^{5}}{x^{5} - 7} + 2\right)}{\sqrt{x^{5} - 7}}
Simplify
    © Mister Exam – Calculator