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Derivative of:
Derivative of e^cos(x)
Derivative of ln(x+3)^3
Derivative of cos(3*x)^(2)
Derivative of -cos(2*x)
Identical expressions
y=(x^ three + six)(x- two)
y equally (x cubed plus 6)(x minus 2)
y equally (x to the power of three plus six)(x minus two)
y=(x3+6)(x-2)
y=x3+6x-2
y=(x³+6)(x-2)
y=(x to the power of 3+6)(x-2)
y=x^3+6x-2
Similar expressions
y=(x^3+6)(x+2)
y=(x^3-6)(x-2)

The derivative of the function/ y=(x^3+6)(x-2)

Derivative of y=(x^3+6)(x-2)

The solution

You have entered [src]

/ 3    \        
\x  + 6/*(x - 2)

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

(x^3 + 6)*(x - 2)

Detail solution

Apply the product rule:

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

$f{\left(x \right)} = x^{3} + 6$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $x^{3} + 6$ term by term:
  1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
  2. The derivative of the constant $6$ is zero.
  The result is: $3 x^{2}$
$g{\left(x \right)} = x - 2$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $x - 2$ term by term:
  1. Apply the power rule: $x$ goes to $1$
  2. The derivative of the constant $-2$ is zero.
  The result is: $1$
The result is: $x^{3} + 3 x^{2} \left(x - 2\right) + 6$
Now simplify:

$4 x^{3} - 6 x^{2} + 6$

The answer is:

$4 x^{3} - 6 x^{2} + 6$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     3      2        
6 + x  + 3*x *(x - 2)

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

Simplify

The second derivative [src]

6*x*(-2 + 2*x)

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

Simplify

The third derivative [src]

12*(-1 + 2*x)

$$12 \left(2 x - 1\right)$$

Simplify

The graph

Derivative of y=(x^3+6)(x-2)