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Derivative of:
Derivative of y=(x+2)²(2x-1)³
Derivative of x-6
Derivative of x^6+x-1/x^2
Derivative of x^5/5
Identical expressions
(4x^ two - eight x+8)^ three
(4x squared minus 8x plus 8) cubed
(4x to the power of two minus eight x plus 8) to the power of three
(4x2-8x+8)3
4x2-8x+83
(4x²-8x+8)³
(4x to the power of 2-8x+8) to the power of 3
4x^2-8x+8^3
Similar expressions
(4x^2+8x+8)^3
(4x^2-8x-8)^3

The derivative of the function/ (4x^2-8x+8)^3

Derivative of (4x^2-8x+8)^3

The solution

You have entered [src]

                3
/   2          \ 
\4*x  - 8*x + 8/

$$\left(4 x^{2} - 8 x + 8\right)^{3}$$

  /                3\
d |/   2          \ |
--\\4*x  - 8*x + 8/ /
dx

$$\frac{d}{d x} \left(4 x^{2} - 8 x + 8\right)^{3}$$

Transform

Detail solution

Let $u = 4 x^{2} - 8 x + 8$ .
Apply the power rule: $u^{3}$ goes to $3 u^{2}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(4 x^{2} - 8 x + 8\right)$ :
1. Differentiate $4 x^{2} - 8 x + 8$ term by term:
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x^{2}$ goes to $2 x$
    So, the result is: $8 x$
  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: $8$
    So, the result is: $-8$
  3. The derivative of the constant $8$ is zero.
  The result is: $8 x - 8$
The result of the chain rule is:

$3 \cdot \left(8 x - 8\right) \left(4 x^{2} - 8 x + 8\right)^{2}$
Now simplify:

$384 \left(x - 1\right) \left(x^{2} - 2 x + 2\right)^{2}$

The answer is:

$384 \left(x - 1\right) \left(x^{2} - 2 x + 2\right)^{2}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

                2             
/   2          \              
\4*x  - 8*x + 8/ *(-24 + 24*x)

$$\left(24 x - 24\right) \left(4 x^{2} - 8 x + 8\right)^{2}$$

Simplify

The second derivative [src]

    /     2      \ /     2                   2\
384*\2 + x  - 2*x/*\2 + x  - 2*x + 4*(-1 + x) /

$$384 \left(x^{2} - 2 x + 2\right) \left(x^{2} - 2 x + 4 \left(x - 1\right)^{2} + 2\right)$$

Simplify

The third derivative [src]

              /                    2      2\
1536*(-1 + x)*\6 - 6*x + 2*(-1 + x)  + 3*x /

$$1536 \left(x - 1\right) \left(3 x^{2} - 6 x + 2 \left(x - 1\right)^{2} + 6\right)$$

Simplify

3-я производная [src]

              /                    2      2\
1536*(-1 + x)*\6 - 6*x + 2*(-1 + x)  + 3*x /

$$1536 \left(x - 1\right) \left(3 x^{2} - 6 x + 2 \left(x - 1\right)^{2} + 6\right)$$

Simplify

The graph

Derivative of (4x^2-8x+8)^3