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Derivative of:
Derivative of f(x)=5
Derivative of y=x^3-8x^2+10x-4
Derivative of y=3x^3
Derivative of y=(x^3-3)(x^2+4x+1)
Graphing y =:
x^2*(x-4)
Identical expressions
x^ two *(x- four)
x squared multiply by (x minus 4)
x to the power of two multiply by (x minus four)
x2*(x-4)
x2*x-4
x²*(x-4)
x to the power of 2*(x-4)
x^2(x-4)
x2(x-4)
x2x-4
x^2x-4
Similar expressions
x^2*(x+4)

The derivative of the function/ x^2*(x-4)

Derivative of x^2*(x-4)

The solution

You have entered [src]

 2        
x *(x - 4)

$$x^{2} \left(x - 4\right)$$

x^2*(x - 4)

Detail solution

Apply the product rule:

$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$

$f{\left(x \right)} = x^{2}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $x^{2}$ goes to $2 x$
$g{\left(x \right)} = x - 4$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $x - 4$ term by term:
  1. Apply the power rule: $x$ goes to $1$
  2. The derivative of the constant $-4$ is zero.
  The result is: $1$
The result is: $x^{2} + 2 x \left(x - 4\right)$
Now simplify:

$x \left(3 x - 8\right)$

The answer is:

$x \left(3 x - 8\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 2              
x  + 2*x*(x - 4)

$$x^{2} + 2 x \left(x - 4\right)$$

Simplify

The second derivative [src]

2*(-4 + 3*x)

$$2 \left(3 x - 4\right)$$

Simplify

The third derivative [src]

$$6$$

Simplify

The graph

Derivative of x^2*(x-4)