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(x^2+7x-1)^3
The derivative of the function/ (x^2+7x-1)^3

Derivative of (x^2+7x-1)^3

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
              3
/ 2          \ 
\x  + 7*x - 1/
$$\left(x^{2} + 7 x - 1\right)^{3}$$ 
  /              3\
d |/ 2          \ |
--\\x  + 7*x - 1/ /
dx
$$\frac{d}{d x} \left(x^{2} + 7 x - 1\right)^{3}$$
Transform
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. 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:

      3. 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
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
              2           
/ 2          \            
\x  + 7*x - 1/ *(21 + 6*x)
$$\left(6 x + 21\right) \left(x^{2} + 7 x - 1\right)^{2}$$
Simplify
The second derivative [src] 
  /      2      \ /      2            2      \
6*\-1 + x  + 7*x/*\-1 + x  + (7 + 2*x)  + 7*x/
$$6 \left(x^{2} + 7 x - 1\right) \left(x^{2} + 7 x + \left(2 x + 7\right)^{2} - 1\right)$$
Simplify
The third derivative [src] 
            /              2      2       \
6*(7 + 2*x)*\-6 + (7 + 2*x)  + 6*x  + 42*x/
$$6 \cdot \left(2 x + 7\right) \left(6 x^{2} + 42 x + \left(2 x + 7\right)^{2} - 6\right)$$
Simplify
The graph
Derivative of (x^2+7x-1)^3
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