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(x^2+4x-1)^6

Derivative of (x^2+4x-1)^6

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
              6
/ 2          \ 
\x  + 4*x - 1/ 
$$\left(\left(x^{2} + 4 x\right) - 1\right)^{6}$$
(x^2 + 4*x - 1)^6
Detail solution
  1. Let .

  2. Apply the power rule: goes to

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

    1. Differentiate term by term:

      1. Differentiate term by term:

        1. Apply the power rule: goes to

        2. The derivative of a constant times a function is the constant times the derivative of the function.

          1. Apply the power rule: goes to

          So, the result is:

        The result is:

      2. The derivative of the constant is zero.

      The result is:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
              5            
/ 2          \             
\x  + 4*x - 1/ *(24 + 12*x)
$$\left(12 x + 24\right) \left(\left(x^{2} + 4 x\right) - 1\right)^{5}$$
The second derivative [src]
                  4                              
   /      2      \  /      2                   2\
12*\-1 + x  + 4*x/ *\-1 + x  + 4*x + 10*(2 + x) /
$$12 \left(x^{2} + 4 x - 1\right)^{4} \left(x^{2} + 4 x + 10 \left(x + 2\right)^{2} - 1\right)$$
The third derivative [src]
                   3                                        
    /      2      \          /        2            2       \
120*\-1 + x  + 4*x/ *(2 + x)*\-3 + 3*x  + 8*(2 + x)  + 12*x/
$$120 \left(x + 2\right) \left(x^{2} + 4 x - 1\right)^{3} \left(3 x^{2} + 12 x + 8 \left(x + 2\right)^{2} - 3\right)$$
The graph
Derivative of (x^2+4x-1)^6