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Derivative of 1/x^5
Derivative of x^5*cos(x)
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Derivative of x-3
Identical expressions
y=(x^ three -6x^ two + three x- one)^ two /3
y equally (x cubed minus 6x squared plus 3x minus 1) squared divide by 3
y equally (x to the power of three minus 6x to the power of two plus three x minus one) to the power of two divide by 3
y=(x3-6x2+3x-1)2/3
y=x3-6x2+3x-12/3
y=(x³-6x²+3x-1)²/3
y=(x to the power of 3-6x to the power of 2+3x-1) to the power of 2/3
y=x^3-6x^2+3x-1^2/3
y=(x^3-6x^2+3x-1)^2 divide by 3
Similar expressions
y=(x^3-6x^2-3x-1)^2/3
y=(x^3+6x^2+3x-1)^2/3
y=(x^3-6x^2+3x+1)^2/3
What you mean?
(x^3 - 6*x^2 + 3*x - 1*1)^2/3
(x^3 - 6*x^2 + 3*x - 1*1)^(2/3)
(x^3 - 6*x^2 + 3*x - 1*1)^(2/3)

The derivative of the function/ y=(x^3-6x^2+3x-1)^2/3

You entered:

y=(x^3-6x^2+3x-1)^2/3

What you mean?

(x^3 - 6*x^2 + 3*x - 1*1)^2/3

(x^3 - 6*x^2 + 3*x - 1*1)^(2/3)

(x^3 - 6*x^2 + 3*x - 1*1)^(2/3)

Derivative of y=(x^3-6x^2+3x-1)^2/3

The solution

You have entered [src]

                     2
/ 3      2          \ 
\x  - 6*x  + 3*x - 1/ 
----------------------
          3

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

  /                     2\
  |/ 3      2          \ |
d |\x  - 6*x  + 3*x - 1/ |
--|----------------------|
dx\          3           /

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

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = x^{3} - 6 x^{2} + 3 x - 1$ .
2. Apply the power rule: $u^{2}$ goes to $2 u$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{3} - 6 x^{2} + 3 x - 1\right)$ :
  1. Differentiate $x^{3} - 6 x^{2} + 3 x - 1$ term by term:
    1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
    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.
        
        Apply the power rule: $x^{2}$ goes to $2 x$
        
        So, the result is: $12 x$
      So, the result is: $- 12 x$
    3. 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: $3$
    4. The derivative of the constant $\left(-1\right) 1$ is zero.
    The result is: $3 x^{2} - 12 x + 3$
  The result of the chain rule is:
  
  $\left(3 x^{2} - 12 x + 3\right) \left(2 x^{3} - 12 x^{2} + 6 x - 2\right)$
So, the result is: $\frac{\left(3 x^{2} - 12 x + 3\right) \left(2 x^{3} - 12 x^{2} + 6 x - 2\right)}{3}$
Now simplify:

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

The answer is:

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

The graph

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The first derivative [src]

/              2\ / 3      2          \
\6 - 24*x + 6*x /*\x  - 6*x  + 3*x - 1/
---------------------------------------
                   3

$$\frac{\left(6 x^{2} - 24 x + 6\right) \left(x^{3} - 6 x^{2} + 3 x - 1\right)}{3}$$

Simplify

The second derivative [src]

  /                2                                    \
  |  /     2      \               /      3      2      \|
2*\3*\1 + x  - 4*x/  + 2*(-2 + x)*\-1 + x  - 6*x  + 3*x//

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

Simplify

The third derivative [src]

  /      3      2                    /     2      \\
4*\-1 + x  - 6*x  + 3*x + 9*(-2 + x)*\1 + x  - 4*x//

$$4 \left(x^{3} - 6 x^{2} + 3 x + 9 \left(x - 2\right) \left(x^{2} - 4 x + 1\right) - 1\right)$$

Simplify

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What you mean?

Derivative of y=(x^3-6x^2+3x-1)^2/3

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The solution