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Identical expressions
y=(x^ four + one)^ five
y equally (x to the power of 4 plus 1) to the power of 5
y equally (x to the power of four plus one) to the power of five
y=(x4+1)5
y=x4+15
y=(x⁴+1)⁵
y=x^4+1^5
Similar expressions
y=(x^4-1)^5

The derivative of the function/ y=(x^4+1)^5

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

The solution

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        5
/ 4    \ 
\x  + 1/

$$\left(x^{4} + 1\right)^{5}$$

(x^4 + 1)^5

Detail solution

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

$20 x^{3} \left(x^{4} + 1\right)^{4}$
Now simplify:

$20 x^{3} \left(x^{4} + 1\right)^{4}$

The answer is:

$20 x^{3} \left(x^{4} + 1\right)^{4}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

              4
    3 / 4    \ 
20*x *\x  + 1/

$$20 x^{3} \left(x^{4} + 1\right)^{4}$$

Simplify

The second derivative [src]

              3            
    2 /     4\  /        4\
20*x *\1 + x / *\3 + 19*x /

$$20 x^{2} \left(x^{4} + 1\right)^{3} \left(19 x^{4} + 3\right)$$

Simplify

The third derivative [src]

              2 /        2                         \
      /     4\  |/     4\        8       4 /     4\|
120*x*\1 + x / *\\1 + x /  + 32*x  + 24*x *\1 + x //

$$120 x \left(x^{4} + 1\right)^{2} \left(32 x^{8} + 24 x^{4} \left(x^{4} + 1\right) + \left(x^{4} + 1\right)^{2}\right)$$

Simplify

The graph

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

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The solution