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Identical expressions
y= two x^ three +6x^2+ three
y equally 2x cubed plus 6x squared plus 3
y equally two x to the power of three plus 6x squared plus three
y=2x3+6x2+3
y=2x³+6x²+3
y=2x to the power of 3+6x to the power of 2+3
Similar expressions
y=2x^3+6x^2-3
y=2x^3-6x^2+3

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

Derivative of y=2x^3+6x^2+3

The solution

You have entered [src]

   3      2    
2*x  + 6*x  + 3

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

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

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

Transform

Detail solution

Differentiate $2 x^{3} + 6 x^{2} + 3$ 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: $x^{3}$ goes to $3 x^{2}$
  So, the result is: $6 x^{2}$
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: $12 x$
3. The derivative of the constant $3$ is zero.
The result is: $6 x^{2} + 12 x$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   2       
6*x  + 12*x

$$6 x^{2} + 12 x$$

Simplify

The second derivative [src]

12*(1 + x)

$$12 \left(x + 1\right)$$

Simplify

The third derivative [src]

$$12$$

Simplify

The graph

Derivative of y=2x^3+6x^2+3