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Identical expressions
(x^ two -3x+ one)^ seven
(x squared minus 3x plus 1) to the power of 7
(x to the power of two minus 3x plus one) to the power of seven
(x2-3x+1)7
x2-3x+17
(x²-3x+1)⁷
(x to the power of 2-3x+1) to the power of 7
x^2-3x+1^7
Similar expressions
(x^2+3x+1)^7
(x^2-3x-1)^7

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

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

The solution

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              7
/ 2          \ 
\x  - 3*x + 1/

$$\left(x^{2} - 3 x + 1\right)^{7}$$

  /              7\
d |/ 2          \ |
--\\x  - 3*x + 1/ /
dx

$$\frac{d}{d x} \left(x^{2} - 3 x + 1\right)^{7}$$

Transform

Detail solution

Let $u = x^{2} - 3 x + 1$ .
Apply the power rule: $u^{7}$ goes to $7 u^{6}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{2} - 3 x + 1\right)$ :
1. Differentiate $x^{2} - 3 x + 1$ term by term:
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. The derivative of a constant times a function is the constant times the derivative of the function.
      1. Apply the power rule: $x$ goes to $1$
      So, the result is: $3$
    So, the result is: $-3$
  3. The derivative of the constant $1$ is zero.
  The result is: $2 x - 3$
The result of the chain rule is:

$7 \cdot \left(2 x - 3\right) \left(x^{2} - 3 x + 1\right)^{6}$
Now simplify:

$\left(14 x - 21\right) \left(x^{2} - 3 x + 1\right)^{6}$

The answer is:

$\left(14 x - 21\right) \left(x^{2} - 3 x + 1\right)^{6}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

              6             
/ 2          \              
\x  - 3*x + 1/ *(-21 + 14*x)

$$\left(14 x - 21\right) \left(x^{2} - 3 x + 1\right)^{6}$$

Simplify

The second derivative [src]

                 5                               
   /     2      \  /     2                     2\
14*\1 + x  - 3*x/ *\1 + x  - 3*x + 3*(-3 + 2*x) /

$$14 \left(x^{2} - 3 x + 1\right)^{5} \left(x^{2} + 3 \left(2 x - 3\right)^{2} - 3 x + 1\right)$$

Simplify

The third derivative [src]

                 4                                             
   /     2      \             /                       2      2\
42*\1 + x  - 3*x/ *(-3 + 2*x)*\6 - 18*x + 5*(-3 + 2*x)  + 6*x /

$$42 \cdot \left(2 x - 3\right) \left(x^{2} - 3 x + 1\right)^{4} \cdot \left(6 x^{2} + 5 \left(2 x - 3\right)^{2} - 18 x + 6\right)$$

Simplify

The graph

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

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The solution