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The derivative of the function/ 3x^4-4x^3+1

Derivative of 3x^4-4x^3+1

Function f() - derivative -N order at the point
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The solution

You have entered [src] 
   4      3    
3*x  - 4*x  + 1
(3x4−4x3)+1\left(3 x^{4} - 4 x^{3}\right) + 1 
3*x^4 - 4*x^3 + 1
Detail solution

  1. Differentiate (3x4−4x3)+1\left(3 x^{4} - 4 x^{3}\right) + 1 term by term:

    1. Differentiate 3x4−4x33 x^{4} - 4 x^{3} term by term:

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

        1. Apply the power rule: x4x^{4} goes to 4x34 x^{3}

        So, the result is: 12x312 x^{3}

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

        1. Apply the power rule: x3x^{3} goes to 3x23 x^{2}

        So, the result is: −12x2- 12 x^{2}

      The result is: 12x3−12x212 x^{3} - 12 x^{2}

    2. The derivative of the constant 11 is zero.

    The result is: 12x3−12x212 x^{3} - 12 x^{2}

  2. Now simplify:

    12x2(x−1)12 x^{2} \left(x - 1\right)

The answer is:

12x2(x−1)12 x^{2} \left(x - 1\right)

The graph
02468-8-6-4-2-1010-5000050000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      2       3
- 12*x  + 12*x
12x3−12x212 x^{3} - 12 x^{2}
Simplify
The second derivative [src] 
12*x*(-2 + 3*x)
12x(3x−2)12 x \left(3 x - 2\right)
Simplify
The third derivative [src] 
24*(-1 + 3*x)
24(3x−1)24 \left(3 x - 1\right)
Simplify
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