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Derivative of:
Derivative of x^-2
Derivative of (-1)/x^2
Derivative of e^x^3
Derivative of (x+1)
Identical expressions
(((x^ two)^ three)^ four)
(((x squared ) cubed ) to the power of 4)
(((x to the power of two) to the power of three) to the power of four)
(((x2)3)4)
x234
(((x²)³)⁴)
(((x to the power of 2) to the power of 3) to the power of 4)
x^2^3^4

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

Derivative of (((x^2)^3)^4)

The solution

You have entered [src]

       4
/    3\ 
|/ 2\ | 
\\x / /

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

((x^2)^3)^4

Detail solution

Let $u = \left(x^{2}\right)^{3}$ .
Apply the power rule: $u^{4}$ goes to $4 u^{3}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{2}\right)^{3}$ :
1. Let $u = x^{2}$ .
2. Apply the power rule: $u^{3}$ goes to $3 u^{2}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{2}$ :
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  The result of the chain rule is:
  
  $6 x^{5}$
The result of the chain rule is:

$24 x^{23}$

The answer is:

$24 x^{23}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    24
24*x  
------
  x

$$\frac{24 x^{24}}{x}$$

Simplify

The second derivative [src]

     22
552*x

$$552 x^{22}$$

Simplify

The third derivative [src]

       21
12144*x

$$12144 x^{21}$$

Simplify