Mister Exam

Lang:

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

Derivative of 3x^2+6x

The solution

You have entered [src]

   2      
3*x  + 6*x

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

d /   2      \
--\3*x  + 6*x/
dx

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

Transform

Detail solution

Differentiate $3 x^{2} + 6 x$ term by term:
1. 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: $6 x$
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: $6$
The result is: $6 x + 6$

The answer is:

$6 x + 6$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

6 + 6*x

$$6 x + 6$$

Simplify

The second derivative [src]

$$6$$

Simplify

The third derivative [src]

$$0$$

Simplify

The graph

Derivative of 3x^2+6x