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Derivative of (x-4)
Factor polynomial:
x^7+4*x^6+4*x^5+2*x^4+4*x^3+3*x^2+3*x+4
Identical expressions
x^ seven + four *x^ six + four *x^ five + two *x^ four + four *x^ three + three *x^ two + three *x+ four
x to the power of 7 plus 4 multiply by x to the power of 6 plus 4 multiply by x to the power of 5 plus 2 multiply by x to the power of 4 plus 4 multiply by x cubed plus 3 multiply by x squared plus 3 multiply by x plus 4
x to the power of seven plus four multiply by x to the power of six plus four multiply by x to the power of five plus two multiply by x to the power of four plus four multiply by x to the power of three plus three multiply by x to the power of two plus three multiply by x plus four
x7+4*x6+4*x5+2*x4+4*x3+3*x2+3*x+4
x⁷+4*x⁶+4*x⁵+2*x⁴+4*x³+3*x²+3*x+4
x to the power of 7+4*x to the power of 6+4*x to the power of 5+2*x to the power of 4+4*x to the power of 3+3*x to the power of 2+3*x+4
x^7+4x^6+4x^5+2x^4+4x^3+3x^2+3x+4
x7+4x6+4x5+2x4+4x3+3x2+3x+4
Similar expressions
x^7+4*x^6+4*x^5+2*x^4+4*x^3+3*x^2+3*x-4
x^7+4*x^6+4*x^5+2*x^4-4*x^3+3*x^2+3*x+4
x^7-4*x^6+4*x^5+2*x^4+4*x^3+3*x^2+3*x+4
x^7+4*x^6+4*x^5+2*x^4+4*x^3-3*x^2+3*x+4
x^7+4*x^6+4*x^5-2*x^4+4*x^3+3*x^2+3*x+4
x^7+4*x^6+4*x^5+2*x^4+4*x^3+3*x^2-3*x+4
x^7+4*x^6-4*x^5+2*x^4+4*x^3+3*x^2+3*x+4

The derivative of the function/ x^7+4*x^6+4*x^5+2*x^4+4*x^3+3*x^2+3*x+4

Derivative of x^7+4x^6+4x^5+2x^4+4x^3+3x^2+3x+4

The solution

You have entered [src]

 7      6      5      4      3      2          
x  + 4*x  + 4*x  + 2*x  + 4*x  + 3*x  + 3*x + 4

$$\left(3 x + \left(3 x^{2} + \left(4 x^{3} + \left(2 x^{4} + \left(4 x^{5} + \left(x^{7} + 4 x^{6}\right)\right)\right)\right)\right)\right) + 4$$

x^7 + 4*x^6 + 4*x^5 + 2*x^4 + 4*x^3 + 3*x^2 + 3*x + 4

Detail solution

Differentiate $\left(3 x + \left(3 x^{2} + \left(4 x^{3} + \left(2 x^{4} + \left(4 x^{5} + \left(x^{7} + 4 x^{6}\right)\right)\right)\right)\right)\right) + 4$ term by term:
1. Differentiate $3 x + \left(3 x^{2} + \left(4 x^{3} + \left(2 x^{4} + \left(4 x^{5} + \left(x^{7} + 4 x^{6}\right)\right)\right)\right)\right)$ term by term:
  1. Differentiate $3 x^{2} + \left(4 x^{3} + \left(2 x^{4} + \left(4 x^{5} + \left(x^{7} + 4 x^{6}\right)\right)\right)\right)$ term by term:
    1. Differentiate $4 x^{3} + \left(2 x^{4} + \left(4 x^{5} + \left(x^{7} + 4 x^{6}\right)\right)\right)$ term by term:
      1. Differentiate $2 x^{4} + \left(4 x^{5} + \left(x^{7} + 4 x^{6}\right)\right)$ term by term:
        
        Differentiate $4 x^{5} + \left(x^{7} + 4 x^{6}\right)$ term by term:
        
        Differentiate $x^{7} + 4 x^{6}$ term by term:
        
        Apply the power rule: $x^{7}$ goes to $7 x^{6}$
        
        The derivative of a constant times a function is the constant times the derivative of the function.
        
        Apply the power rule: $x^{6}$ goes to $6 x^{5}$
        
        So, the result is: $24 x^{5}$
        
        The result is: $7 x^{6} + 24 x^{5}$
        
        The derivative of a constant times a function is the constant times the derivative of the function.
        
        Apply the power rule: $x^{5}$ goes to $5 x^{4}$
        
        So, the result is: $20 x^{4}$
        
        The result is: $7 x^{6} + 24 x^{5} + 20 x^{4}$
        
        The derivative of a constant times a function is the constant times the derivative of the function.
        
        Apply the power rule: $x^{4}$ goes to $4 x^{3}$
        
        So, the result is: $8 x^{3}$
        
        The result is: $7 x^{6} + 24 x^{5} + 20 x^{4} + 8 x^{3}$
      2. The derivative of a constant times a function is the constant times the derivative of the function.
        
        Apply the power rule: $x^{3}$ goes to $3 x^{2}$
        
        So, the result is: $12 x^{2}$
      The result is: $7 x^{6} + 24 x^{5} + 20 x^{4} + 8 x^{3} + 12 x^{2}$
    2. The derivative of a constant times a function is the constant times the derivative of the function.
      1. Apply the power rule: $x^{2}$ goes to $2 x$
      So, the result is: $6 x$
    The result is: $7 x^{6} + 24 x^{5} + 20 x^{4} + 8 x^{3} + 12 x^{2} + 6 x$
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x$ goes to $1$
    So, the result is: $3$
  The result is: $7 x^{6} + 24 x^{5} + 20 x^{4} + 8 x^{3} + 12 x^{2} + 6 x + 3$
2. The derivative of the constant $4$ is zero.
The result is: $7 x^{6} + 24 x^{5} + 20 x^{4} + 8 x^{3} + 12 x^{2} + 6 x + 3$

The answer is:

$7 x^{6} + 24 x^{5} + 20 x^{4} + 8 x^{3} + 12 x^{2} + 6 x + 3$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

             6      3       2       4       5
3 + 6*x + 7*x  + 8*x  + 12*x  + 20*x  + 24*x

$$7 x^{6} + 24 x^{5} + 20 x^{4} + 8 x^{3} + 12 x^{2} + 6 x + 3$$

Simplify

The second derivative [src]

  /               2       5       3       4\
2*\3 + 12*x + 12*x  + 21*x  + 40*x  + 60*x /

$$2 \left(21 x^{5} + 60 x^{4} + 40 x^{3} + 12 x^{2} + 12 x + 3\right)$$

Simplify

The third derivative [src]

  /              4       2       3\
6*\4 + 8*x + 35*x  + 40*x  + 80*x /

$$6 \left(35 x^{4} + 80 x^{3} + 40 x^{2} + 8 x + 4\right)$$

Simplify

5-я производная [src]

    /        2       \
120*\4 + 21*x  + 24*x/

$$120 \left(21 x^{2} + 24 x + 4\right)$$

Simplify

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Derivative of x^7+4x^6+4x^5+2x^4+4x^3+3x^2+3x+4

The graph:

Piecewise:

The solution

Other calculators

How to use it?

Identical expressions

Similar expressions

Derivative of x^7+4*x^6+4*x^5+2*x^4+4*x^3+3*x^2+3*x+4

The graph:

Piecewise:

The solution

Derivative of x^7+4x^6+4x^5+2x^4+4x^3+3x^2+3x+4