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Derivative of:
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Graphing y =:
x^3-6x^2+5
Identical expressions
x^ three -6x^ two + five
x cubed minus 6x squared plus 5
x to the power of three minus 6x to the power of two plus five
x3-6x2+5
x³-6x²+5
x to the power of 3-6x to the power of 2+5
Similar expressions
x^3+6x^2+5
x^3-6x^2-5

The derivative of the function/ x^3-6x^2+5

Derivative of x^3-6x^2+5

The solution

You have entered [src]

 3      2    
x  - 6*x  + 5

$$\left(x^{3} - 6 x^{2}\right) + 5$$

x^3 - 6*x^2 + 5

Detail solution

Differentiate $\left(x^{3} - 6 x^{2}\right) + 5$ term by term:
1. Differentiate $x^{3} - 6 x^{2}$ 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: $- 12 x$
  The result is: $3 x^{2} - 12 x$
2. The derivative of the constant $5$ is zero.
The result is: $3 x^{2} - 12 x$
Now simplify:

$3 x \left(x - 4\right)$

The answer is:

$3 x \left(x - 4\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

           2
-12*x + 3*x

$$3 x^{2} - 12 x$$

Simplify

The second derivative [src]

6*(-2 + x)

$$6 \left(x - 2\right)$$

Simplify

The third derivative [src]

$$6$$

Simplify

The graph

Derivative of x^3-6x^2+5