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Derivative of:
Derivative of (x^2+1)^3
Derivative of (x+3)/(x-2)
Derivative of u
Derivative of (x-1)/2
Identical expressions
(3x^ two -3x)^ five
(3x squared minus 3x) to the power of 5
(3x to the power of two minus 3x) to the power of five
(3x2-3x)5
3x2-3x5
(3x²-3x)⁵
(3x to the power of 2-3x) to the power of 5
3x^2-3x^5
Similar expressions
(3x^2+3x)^5

The derivative of the function/ (3x^2-3x)^5

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

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

$$\frac{d}{d x} \left(3 x^{2} - 3 x\right)^{5}$$

Transform

Detail solution

Let $u = 3 x^{2} - 3 x$ .
Apply the power rule: $u^{5}$ goes to $5 u^{4}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(3 x^{2} - 3 x\right)$ :
1. Differentiate $3 x^{2} - 3 x$ 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: $6 x$
  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: $x$ goes to $1$
      So, the result is: $3$
    So, the result is: $-3$
  The result is: $6 x - 3$
The result of the chain rule is:

$5 \cdot \left(6 x - 3\right) \left(3 x^{2} - 3 x\right)^{4}$
Now simplify:

$x^{4} \left(x - 1\right)^{4} \cdot \left(2430 x - 1215\right)$

The answer is:

$x^{4} \left(x - 1\right)^{4} \cdot \left(2430 x - 1215\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

            4             
/   2      \              
\3*x  - 3*x/ *(-15 + 30*x)

$$\left(30 x - 15\right) \left(3 x^{2} - 3 x\right)^{4}$$

Simplify

The second derivative [src]

      3         3 /            2             \
2430*x *(-1 + x) *\2*(-1 + 2*x)  + x*(-1 + x)/

$$2430 x^{3} \left(x - 1\right)^{3} \left(x \left(x - 1\right) + 2 \left(2 x - 1\right)^{2}\right)$$

Simplify

The third derivative [src]

       2         2            /          2               \
14580*x *(-1 + x) *(-1 + 2*x)*\(-1 + 2*x)  + 2*x*(-1 + x)/

$$14580 x^{2} \left(x - 1\right)^{2} \cdot \left(2 x - 1\right) \left(2 x \left(x - 1\right) + \left(2 x - 1\right)^{2}\right)$$

Simplify

The graph

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