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Derivative of (x^2-4)^3
Derivative of (x+4)^1/2
Derivative of x^3*cot(4*x)
Derivative of x^3-9x^2+7
Identical expressions
x^ three -9x^ two + seven
x cubed minus 9x squared plus 7
x to the power of three minus 9x to the power of two plus seven
x3-9x2+7
x³-9x²+7
x to the power of 3-9x to the power of 2+7
Similar expressions
x^3-9x^2-7
x^3+9x^2+7

The derivative of the function/ x^3-9x^2+7

Derivative of x^3-9x^2+7

The solution

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 3      2    
x  - 9*x  + 7

$$\left(x^{3} - 9 x^{2}\right) + 7$$

x^3 - 9*x^2 + 7

Detail solution

Differentiate $\left(x^{3} - 9 x^{2}\right) + 7$ term by term:
1. Differentiate $x^{3} - 9 x^{2}$ 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: $- 18 x$
  The result is: $3 x^{2} - 18 x$
2. The derivative of the constant $7$ is zero.
The result is: $3 x^{2} - 18 x$
Now simplify:

$3 x \left(x - 6\right)$

The answer is:

$3 x \left(x - 6\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

           2
-18*x + 3*x

$$3 x^{2} - 18 x$$

Simplify

The second derivative [src]

6*(-3 + x)

$$6 \left(x - 3\right)$$

Simplify

The third derivative [src]

$$6$$

Simplify

The graph

Derivative of x^3-9x^2+7