Mister Exam

Derivative of (3x²+1)³

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
          3
/   2    \ 
\3*x  + 1/ 
$$\left(3 x^{2} + 1\right)^{3}$$
  /          3\
d |/   2    \ |
--\\3*x  + 1/ /
dx             
$$\frac{d}{d x} \left(3 x^{2} + 1\right)^{3}$$
Detail solution
  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    1. Differentiate 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: goes to

        So, the result is:

      2. The derivative of the constant is zero.

      The result is:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
               2
     /   2    \ 
18*x*\3*x  + 1/ 
$$18 x \left(3 x^{2} + 1\right)^{2}$$
The second derivative [src]
   /       2\ /        2\
18*\1 + 3*x /*\1 + 15*x /
$$18 \cdot \left(3 x^{2} + 1\right) \left(15 x^{2} + 1\right)$$
The third derivative [src]
      /       2\
648*x*\1 + 5*x /
$$648 x \left(5 x^{2} + 1\right)$$
The graph
Derivative of (3x²+1)³