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Derivative of:
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Derivative of 3*sqrt(x)
Graphing y =:
x^3+3x^2-9x
Identical expressions
x^ three +3x^ two -9x
x cubed plus 3x squared minus 9x
x to the power of three plus 3x to the power of two minus 9x
x3+3x2-9x
x³+3x²-9x
x to the power of 3+3x to the power of 2-9x
Similar expressions
x^3+3x^2+9x
x^3-3x^2-9x

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

Derivative of x^3+3x^2-9x

The solution

You have entered [src]

 3      2      
x  + 3*x  - 9*x

$$- 9 x + \left(x^{3} + 3 x^{2}\right)$$

x^3 + 3*x^2 - 9*x

Detail solution

Differentiate $- 9 x + \left(x^{3} + 3 x^{2}\right)$ term by term:
1. Differentiate $x^{3} + 3 x^{2}$ term by term:
  1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x^{2}$ goes to $2 x$
    So, the result is: $6 x$
  The result is: $3 x^{2} + 6 x$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x$ goes to $1$
  So, the result is: $-9$
The result is: $3 x^{2} + 6 x - 9$

The answer is:

$3 x^{2} + 6 x - 9$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

        2      
-9 + 3*x  + 6*x

$$3 x^{2} + 6 x - 9$$

Simplify

The second derivative [src]

6*(1 + x)

$$6 \left(x + 1\right)$$

Simplify

The third derivative [src]

$$6$$

Simplify

The graph

Derivative of x^3+3x^2-9x