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f(x)=3x³-4x²
The derivative of the function/ f(x)=3x³-4x²

Derivative of f(x)=3x³-4x²

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

You have entered [src] 
   3      2
3*x  - 4*x
3x3−4x23 x^{3} - 4 x^{2} 
d /   3      2\
--\3*x  - 4*x /
dx
ddx(3x3−4x2)\frac{d}{d x} \left(3 x^{3} - 4 x^{2}\right)
Transform
Detail solution

  1. Differentiate 3x3−4x23 x^{3} - 4 x^{2} 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: 9x29 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: 8x8 x

      So, the result is: −8x- 8 x

    The result is: 9x2−8x9 x^{2} - 8 x

  2. Now simplify:

    x(9x−8)x \left(9 x - 8\right)

The answer is:

x(9x−8)x \left(9 x - 8\right)

The graph
02468-8-6-4-2-1010-50005000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
          2
-8*x + 9*x
9x2−8x9 x^{2} - 8 x
Simplify
The second derivative [src] 
2*(-4 + 9*x)
2⋅(9x−4)2 \cdot \left(9 x - 4\right)
Simplify
The third derivative [src] 
18
1818
Simplify
The graph
Derivative of f(x)=3x³-4x²
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