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Identical expressions
y=x^ five - three x^ four -x^3-5x^ two +x- one
y equally x to the power of 5 minus 3x to the power of 4 minus x cubed minus 5x squared plus x minus 1
y equally x to the power of five minus three x to the power of four minus x cubed minus 5x to the power of two plus x minus one
y=x5-3x4-x3-5x2+x-1
y=x⁵-3x⁴-x³-5x²+x-1
y=x to the power of 5-3x to the power of 4-x to the power of 3-5x to the power of 2+x-1
Similar expressions
y=x^5-3x^4-x^3+5x^2+x-1
y=x^5+3x^4-x^3-5x^2+x-1
y=x^5-3x^4-x^3-5x^2-x-1
y=x^5-3x^4-x^3-5x^2+x+1
y=x^5-3x^4+x^3-5x^2+x-1

The derivative of the function/ y=x^5-3x^4-x^3-5x^2+x-1

Derivative of y=x^5-3x^4-x^3-5x^2+x-1

The solution

You have entered [src]

 5      4    3      2        
x  - 3*x  - x  - 5*x  + x - 1

$$\left(x + \left(- 5 x^{2} + \left(- x^{3} + \left(x^{5} - 3 x^{4}\right)\right)\right)\right) - 1$$

x^5 - 3*x^4 - x^3 - 5*x^2 + x - 1

Detail solution

Differentiate $\left(x + \left(- 5 x^{2} + \left(- x^{3} + \left(x^{5} - 3 x^{4}\right)\right)\right)\right) - 1$ term by term:
1. Differentiate $x + \left(- 5 x^{2} + \left(- x^{3} + \left(x^{5} - 3 x^{4}\right)\right)\right)$ term by term:
  1. Differentiate $- 5 x^{2} + \left(- x^{3} + \left(x^{5} - 3 x^{4}\right)\right)$ term by term:
    1. Differentiate $- x^{3} + \left(x^{5} - 3 x^{4}\right)$ term by term:
      1. Differentiate $x^{5} - 3 x^{4}$ term by term:
        
        Apply the power rule: $x^{5}$ goes to $5 x^{4}$
        
        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: $- 12 x^{3}$
        
        The result is: $5 x^{4} - 12 x^{3}$
      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: $- 3 x^{2}$
      The result is: $5 x^{4} - 12 x^{3} - 3 x^{2}$
    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: $- 10 x$
    The result is: $5 x^{4} - 12 x^{3} - 3 x^{2} - 10 x$
  2. Apply the power rule: $x$ goes to $1$
  The result is: $5 x^{4} - 12 x^{3} - 3 x^{2} - 10 x + 1$
2. The derivative of the constant $-1$ is zero.
The result is: $5 x^{4} - 12 x^{3} - 3 x^{2} - 10 x + 1$

The answer is:

$5 x^{4} - 12 x^{3} - 3 x^{2} - 10 x + 1$

The graph

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The first derivative [src]

        3             2      4
1 - 12*x  - 10*x - 3*x  + 5*x

$$5 x^{4} - 12 x^{3} - 3 x^{2} - 10 x + 1$$

Simplify

The second derivative [src]

  /         2             3\
2*\-5 - 18*x  - 3*x + 10*x /

$$2 \left(10 x^{3} - 18 x^{2} - 3 x - 5\right)$$

Simplify

The third derivative [src]

  /                2\
6*\-1 - 12*x + 10*x /

$$6 \left(10 x^{2} - 12 x - 1\right)$$

Simplify

The graph

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Derivative of y=x^5-3x^4-x^3-5x^2+x-1

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