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(3x^2-3x)^5

Derivative of (3x^2-3x)^5

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
            5
/   2      \ 
\3*x  - 3*x/ 
$$\left(3 x^{2} - 3 x\right)^{5}$$
  /            5\
d |/   2      \ |
--\\3*x  - 3*x/ /
dx               
$$\frac{d}{d x} \left(3 x^{2} - 3 x\right)^{5}$$
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 a constant times a function is the constant times the derivative of the function.

        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:

        So, the result is:

      The result is:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
            4             
/   2      \              
\3*x  - 3*x/ *(-15 + 30*x)
$$\left(30 x - 15\right) \left(3 x^{2} - 3 x\right)^{4}$$
The second derivative [src]
      3         3 /            2             \
2430*x *(-1 + x) *\2*(-1 + 2*x)  + x*(-1 + x)/
$$2430 x^{3} \left(x - 1\right)^{3} \left(x \left(x - 1\right) + 2 \left(2 x - 1\right)^{2}\right)$$
The third derivative [src]
       2         2            /          2               \
14580*x *(-1 + x) *(-1 + 2*x)*\(-1 + 2*x)  + 2*x*(-1 + x)/
$$14580 x^{2} \left(x - 1\right)^{2} \cdot \left(2 x - 1\right) \left(2 x \left(x - 1\right) + \left(2 x - 1\right)^{2}\right)$$
The graph
Derivative of (3x^2-3x)^5