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Derivative of:
Derivative of x^3-4x^2+5x-2
Derivative of ctgx
Derivative of (4x^2-2x+1)^3
Derivative of y=xcos^2x
Identical expressions
(4x^ two -2x+ one)^ three
(4x squared minus 2x plus 1) cubed
(4x to the power of two minus 2x plus one) to the power of three
(4x2-2x+1)3
4x2-2x+13
(4x²-2x+1)³
(4x to the power of 2-2x+1) to the power of 3
4x^2-2x+1^3
Similar expressions
(4x^2-2x-1)^3
(4x^2+2x+1)^3

The derivative of the function/ (4x^2-2x+1)^3

Derivative of (4x^2-2x+1)^3

The solution

You have entered [src]

                3
/   2          \ 
\4*x  - 2*x + 1/

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

  /                3\
d |/   2          \ |
--\\4*x  - 2*x + 1/ /
dx

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

Transform

Detail solution

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

$3 \cdot \left(8 x - 2\right) \left(4 x^{2} - 2 x + 1\right)^{2}$
Now simplify:

$\left(24 x - 6\right) \left(4 x^{2} - 2 x + 1\right)^{2}$

The answer is:

$\left(24 x - 6\right) \left(4 x^{2} - 2 x + 1\right)^{2}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

                2            
/   2          \             
\4*x  - 2*x + 1/ *(-6 + 24*x)

$$\left(24 x - 6\right) \left(4 x^{2} - 2 x + 1\right)^{2}$$

Simplify

The second derivative [src]

   /             2\ /              2            2\
24*\1 - 2*x + 4*x /*\1 + (-1 + 4*x)  - 2*x + 4*x /

$$24 \cdot \left(4 x^{2} - 2 x + 1\right) \left(4 x^{2} + \left(4 x - 1\right)^{2} - 2 x + 1\right)$$

Simplify

The third derivative [src]

              /              2              2\
48*(-1 + 4*x)*\6 + (-1 + 4*x)  - 12*x + 24*x /

$$48 \cdot \left(4 x - 1\right) \left(24 x^{2} + \left(4 x - 1\right)^{2} - 12 x + 6\right)$$

Simplify

The graph

Derivative of (4x^2-2x+1)^3