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Derivative of:
Derivative of x^3/(x^2+5)
Derivative of x^(3/2)-3*x+1
Derivative of (x-1)*e^x
Derivative of sqrt(x)*tan(x)
Identical expressions
(x^ two -2x+ four)^ four
(x squared minus 2x plus 4) to the power of 4
(x to the power of two minus 2x plus four) to the power of four
(x2-2x+4)4
x2-2x+44
(x²-2x+4)⁴
(x to the power of 2-2x+4) to the power of 4
x^2-2x+4^4
Similar expressions
(x^2-2x-4)^4
(x^2+2x+4)^4

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

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

The solution

You have entered [src]

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

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

(x^2 - 2*x + 4)^4

Detail solution

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

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

                2                             
  /     2      \  /     2                   2\
8*\4 + x  - 2*x/ *\4 + x  - 2*x + 6*(-1 + x) /

$$8 \left(x^{2} - 2 x + 4\right)^{2} \left(x^{2} - 2 x + 6 \left(x - 1\right)^{2} + 4\right)$$

Simplify

The third derivative [src]

            /     2      \ /              2             2\
48*(-1 + x)*\4 + x  - 2*x/*\12 - 6*x + 3*x  + 4*(-1 + x) /

$$48 \left(x - 1\right) \left(x^{2} - 2 x + 4\right) \left(3 x^{2} - 6 x + 4 \left(x - 1\right)^{2} + 12\right)$$

Simplify