Mister Exam

Other calculators

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

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

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   3      2          
2*x  - 3*x  + 4*x - 5
2x3−3x2+4x−52 x^{3} - 3 x^{2} + 4 x - 5 
d /   3      2          \
--\2*x  - 3*x  + 4*x - 5/
dx
ddx(2x3−3x2+4x−5)\frac{d}{d x} \left(2 x^{3} - 3 x^{2} + 4 x - 5\right)
Transform
Detail solution

  1. Differentiate 2x3−3x2+4x−52 x^{3} - 3 x^{2} + 4 x - 5 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: x3x^{3} goes to 3x23 x^{2}

      So, the result is: 6x26 x^{2}

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

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

        1. Apply the power rule: x2x^{2} goes to 2x2 x

        So, the result is: 6x6 x

      So, the result is: −6x- 6 x

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

      1. Apply the power rule: xx goes to 11

      So, the result is: 44

    4. The derivative of the constant (−1)5\left(-1\right) 5 is zero.

    The result is: 6x2−6x+46 x^{2} - 6 x + 4

The answer is:

6x2−6x+46 x^{2} - 6 x + 4

The graph
02468-8-6-4-2-1010-50005000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
             2
4 - 6*x + 6*x
6x2−6x+46 x^{2} - 6 x + 4
Simplify
The second derivative [src] 
6*(-1 + 2*x)
6⋅(2x−1)6 \cdot \left(2 x - 1\right)
Simplify
3-th derivative [src] 
12
1212
Simplify
The third derivative [src] 
12
1212
Simplify
The graph
Derivative of 2x^3-3x^2+4x-5
    © Mister Exam – Calculator