Mister Exam

Derivative of f(x)=2x⁴+x³-x²+4

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

The graph:

from to

Piecewise:

The solution

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

    1. Differentiate term by term:

      1. Differentiate 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: goes to

          So, the result is:

        2. Apply the power rule: goes to

        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 answer is:

The graph
The first derivative [src]
          2      3
-2*x + 3*x  + 8*x 
$$8 x^{3} + 3 x^{2} - 2 x$$
The second derivative [src]
  /               2\
2*\-1 + 3*x + 12*x /
$$2 \left(12 x^{2} + 3 x - 1\right)$$
The third derivative [src]
6*(1 + 8*x)
$$6 \left(8 x + 1\right)$$
The graph
Derivative of f(x)=2x⁴+x³-x²+4