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Derivative of:
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Graphing y =:
2*x^2+3*x+1
Factor squared:
2*x^2+3*x+1
Identical expressions
two *x^ two + three *x+ one
2 multiply by x squared plus 3 multiply by x plus 1
two multiply by x to the power of two plus three multiply by x plus one
2*x2+3*x+1
2*x²+3*x+1
2*x to the power of 2+3*x+1
2x^2+3x+1
2x2+3x+1
Similar expressions
2*x^2-3*x+1
2*x^2+3*x-1

The derivative of the function/ 2*x^2+3*x+1

Derivative of 2x^2+3x+1

The solution

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   2          
2*x  + 3*x + 1

$$2 x^{2} + 3 x + 1$$

d /   2          \
--\2*x  + 3*x + 1/
dx

$$\frac{d}{d x} \left(2 x^{2} + 3 x + 1\right)$$

Transform

Detail solution

Differentiate $2 x^{2} + 3 x + 1$ 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: $4 x$
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: $3$
3. The derivative of the constant $1$ is zero.
The result is: $4 x + 3$

The answer is:

$4 x + 3$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

3 + 4*x

$$4 x + 3$$

Simplify

The second derivative [src]

$$4$$

Simplify

3-th derivative [src]

$$0$$

Simplify

The third derivative [src]

$$0$$

Simplify

The graph

Derivative of 2*x^2+3*x+1