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sqrtx^5+1
The derivative of the function/ sqrtx^5+1

Derivative of sqrtx^5+1

Function f() - derivative -N order at the point
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The solution

You have entered [src] 
     5    
  ___     
\/ x   + 1
(x)5+1\left(\sqrt{x}\right)^{5} + 1 
  /     5    \
d |  ___     |
--\\/ x   + 1/
dx
ddx((x)5+1)\frac{d}{d x} \left(\left(\sqrt{x}\right)^{5} + 1\right)
Transform
Detail solution

  1. Differentiate (x)5+1\left(\sqrt{x}\right)^{5} + 1 term by term:

    1. Let u=xu = \sqrt{x}.

    2. Apply the power rule: u5u^{5} goes to 5u45 u^{4}

    3. Then, apply the chain rule. Multiply by ddxx\frac{d}{d x} \sqrt{x}:

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

      The result of the chain rule is:

      5x322\frac{5 x^{\frac{3}{2}}}{2}

    4. The derivative of the constant 11 is zero.

    The result is: 5x322\frac{5 x^{\frac{3}{2}}}{2}

The answer is:

5x322\frac{5 x^{\frac{3}{2}}}{2}

The graph
02468-8-6-4-2-10100500
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   5/2
5*x   
------
 2*x
5x522x\frac{5 x^{\frac{5}{2}}}{2 x}
Simplify
The second derivative [src] 
     ___
15*\/ x 
--------
   4
15x4\frac{15 \sqrt{x}}{4}
Simplify
The third derivative [src] 
   15  
-------
    ___
8*\/ x
158x\frac{15}{8 \sqrt{x}}
Simplify
The graph
Derivative of sqrtx^5+1
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