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x^3-9x^2
The derivative of the function/ x^3-9x^2

Derivative of x^3-9x^2

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

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The solution

You have entered [src] 
 3      2
x  - 9*x
x3−9x2x^{3} - 9 x^{2} 
d / 3      2\
--\x  - 9*x /
dx
ddx(x3−9x2)\frac{d}{d x} \left(x^{3} - 9 x^{2}\right)
Transform
Detail solution

  1. Differentiate x3−9x2x^{3} - 9 x^{2} term by term:

    1. Apply the power rule: x3x^{3} goes to 3x23 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: 18x18 x

      So, the result is: −18x- 18 x

    The result is: 3x2−18x3 x^{2} - 18 x

  2. Now simplify:

    3x(x−6)3 x \left(x - 6\right)

The answer is:

3x(x−6)3 x \left(x - 6\right)

The graph
02468-8-6-4-2-1010-25002500
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
           2
-18*x + 3*x
3x2−18x3 x^{2} - 18 x
Simplify
The second derivative [src] 
6*(-3 + x)
6(x−3)6 \left(x - 3\right)
Simplify
The third derivative [src] 
6
66
Simplify
The graph
Derivative of x^3-9x^2
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