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Derivative of:
Derivative of x*2^x
Derivative of 2*sqrt(x)-4*log(2+sqrt(x))
Derivative of 1/(1-x^2)^2
Derivative of y=2x^3
Identical expressions
x^ three +3x^ two + one
x cubed plus 3x squared plus 1
x to the power of three plus 3x to the power of two plus one
x3+3x2+1
x³+3x²+1
x to the power of 3+3x to the power of 2+1
Similar expressions
x^3+3x^2-1
x^3-3x^2+1

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

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

The solution

You have entered [src]

 3      2    
x  + 3*x  + 1

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

x^3 + 3*x^2 + 1

Detail solution

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

$3 x \left(x + 2\right)$

The answer is:

3 x \left(x + 2\right)

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   2      
3*x  + 6*x

3 x^{2} + 6 x

Simplify

The second derivative [src]

6*(1 + x)

6 \left(x + 1\right)

Simplify

The third derivative [src]

6

Simplify