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Derivative of x^8+x^7

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 8    7
x  + x

$$x^{8} + x^{7}$$

x^8 + x^7

Detail solution

Differentiate $x^{8} + x^{7}$ term by term:
1. Apply the power rule: $x^{8}$ goes to $8 x^{7}$
2. Apply the power rule: $x^{7}$ goes to $7 x^{6}$
The result is: $8 x^{7} + 7 x^{6}$
Now simplify:

$x^{6} \left(8 x + 7\right)$

The answer is:

$x^{6} \left(8 x + 7\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   6      7
7*x  + 8*x

$$8 x^{7} + 7 x^{6}$$

Simplify

The second derivative [src]

    5          
14*x *(3 + 4*x)

$$14 x^{5} \left(4 x + 3\right)$$

Simplify

The third derivative [src]

    4          
42*x *(5 + 8*x)

$$42 x^{4} \left(8 x + 5\right)$$

Simplify

The graph