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y=(x^4+1)^5

Derivative of y=(x^4+1)^5

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
        5
/ 4    \ 
\x  + 1/ 
$$\left(x^{4} + 1\right)^{5}$$
(x^4 + 1)^5
Detail solution
  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    1. Differentiate term by term:

      1. Apply the power rule: goes to

      2. The derivative of the constant is zero.

      The result is:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
              4
    3 / 4    \ 
20*x *\x  + 1/ 
$$20 x^{3} \left(x^{4} + 1\right)^{4}$$
The second derivative [src]
              3            
    2 /     4\  /        4\
20*x *\1 + x / *\3 + 19*x /
$$20 x^{2} \left(x^{4} + 1\right)^{3} \left(19 x^{4} + 3\right)$$
The third derivative [src]
              2 /        2                         \
      /     4\  |/     4\        8       4 /     4\|
120*x*\1 + x / *\\1 + x /  + 32*x  + 24*x *\1 + x //
$$120 x \left(x^{4} + 1\right)^{2} \left(32 x^{8} + 24 x^{4} \left(x^{4} + 1\right) + \left(x^{4} + 1\right)^{2}\right)$$
The graph
Derivative of y=(x^4+1)^5