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x^5+2x^4+3x^3+4x^2+5x+6
The derivative of the function/ x^5+2x^4+3x^3+4x^2+5x+6

Derivative of x^5+2x^4+3x^3+4x^2+5x+6

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 5      4      3      2          
x  + 2*x  + 3*x  + 4*x  + 5*x + 6
$$x^{5} + 2 x^{4} + 3 x^{3} + 4 x^{2} + 5 x + 6$$ 
d / 5      4      3      2          \
--\x  + 2*x  + 3*x  + 4*x  + 5*x + 6/
dx
$$\frac{d}{d x} \left(x^{5} + 2 x^{4} + 3 x^{3} + 4 x^{2} + 5 x + 6\right)$$
Transform
Detail solution

  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:

    3. 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:

    4. 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:

    5. 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:

    6. The derivative of the constant is zero.

    The result is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
       4            3      2
5 + 5*x  + 8*x + 8*x  + 9*x
$$5 x^{4} + 8 x^{3} + 9 x^{2} + 8 x + 5$$
Simplify
The second derivative [src] 
  /              3       2\
2*\4 + 9*x + 10*x  + 12*x /
$$2 \cdot \left(10 x^{3} + 12 x^{2} + 9 x + 4\right)$$
Simplify
The third derivative [src] 
  /              2\
6*\3 + 8*x + 10*x /
$$6 \cdot \left(10 x^{2} + 8 x + 3\right)$$
Simplify
The graph
Derivative of x^5+2x^4+3x^3+4x^2+5x+6
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