Derivative of x^5+x

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 5    
x  + x

$$x^{5} + x$$

x^5 + x

Detail solution

Differentiate $x^{5} + x$ term by term:
1. Apply the power rule: $x^{5}$ goes to $5 x^{4}$
2. Apply the power rule: $x$ goes to $1$
The result is: $5 x^{4} + 1$

The answer is:

$5 x^{4} + 1$

The graph

Plot the graph f(x)

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The first derivative [src]

       4
1 + 5*x

$$5 x^{4} + 1$$

Simplify

The second derivative [src]

    3
20*x

$$20 x^{3}$$

Simplify

The third derivative [src]

    2
60*x

$$60 x^{2}$$

Simplify

The graph