### Other calculators # Derivatives y=x⁸+7x⁷-6x⁶+5x⁵-4x⁴-x³-x²+5

Function f() - derivative -N order

from to

### The solution

You have entered [src]
 8      7      6      5      4    3    2
x  + 7*x  - 6*x  + 5*x  - 4*x  - x  - x  + 5
$$\left(- x^{2} + \left(- x^{3} + \left(- 4 x^{4} + \left(5 x^{5} + \left(- 6 x^{6} + \left(x^{8} + 7 x^{7}\right)\right)\right)\right)\right)\right) + 5$$
x^8 + 7*x^7 - 6*x^6 + 5*x^5 - 4*x^4 - x^3 - x^2 + 5
Detail solution
1. Differentiate term by term:

1. Differentiate term by term:

1. Differentiate term by term:

1. Differentiate term by term:

1. Differentiate term by term:

1. Differentiate term by term:

1. Differentiate term by term:

1. Apply the power rule: goes to

2. The derivative of a constant times a function is the constant times the derivative of the function.

1. Apply the power rule: goes to

So, the result is:

The result is:

2. The derivative of a constant times a function is the constant times the derivative of the function.

1. Apply the power rule: goes to

So, the result is:

The result is:

2. The derivative of a constant times a function is the constant times the derivative of the function.

1. Apply the power rule: goes to

So, the result is:

The result is:

2. The derivative of a constant times a function is the constant times the derivative of the function.

1. Apply the power rule: goes to

So, the result is:

The result is:

2. The derivative of a constant times a function is the constant times the derivative of the function.

1. Apply the power rule: goes to

So, the result is:

The result is:

2. The derivative of a constant times a function is the constant times the derivative of the function.

1. Apply the power rule: goes to

So, the result is:

The result is:

2. The derivative of the constant is zero.

The result is:

2. Now simplify:

The graph
The first derivative [src]
      5       3      2            7       4       6
- 36*x  - 16*x  - 3*x  - 2*x + 8*x  + 25*x  + 49*x 
$$8 x^{7} + 49 x^{6} - 36 x^{5} + 25 x^{4} - 16 x^{3} - 3 x^{2} - 2 x$$
The second derivative [src]
  /         4       2             6       3        5\
2*\-1 - 90*x  - 24*x  - 3*x + 28*x  + 50*x  + 147*x /
$$2 \left(28 x^{6} + 147 x^{5} - 90 x^{4} + 50 x^{3} - 24 x^{2} - 3 x - 1\right)$$
The third derivative [src]
  /          3              2       5        4\
6*\-1 - 120*x  - 16*x + 50*x  + 56*x  + 245*x /
$$6 \left(56 x^{5} + 245 x^{4} - 120 x^{3} + 50 x^{2} - 16 x - 1\right)$$
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