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(x^2-3x)^5

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

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

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Piecewise:

The solution

You have entered [src]
          5
/ 2      \ 
\x  - 3*x/ 
(x23x)5\left(x^{2} - 3 x\right)^{5}
  /          5\
d |/ 2      \ |
--\\x  - 3*x/ /
dx             
ddx(x23x)5\frac{d}{d x} \left(x^{2} - 3 x\right)^{5}
Detail solution
  1. Let u=x23xu = x^{2} - 3 x.

  2. Apply the power rule: u5u^{5} goes to 5u45 u^{4}

  3. Then, apply the chain rule. Multiply by ddx(x23x)\frac{d}{d x} \left(x^{2} - 3 x\right):

    1. Differentiate x23xx^{2} - 3 x term by term:

      1. Apply the power rule: x2x^{2} goes to 2x2 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: xx goes to 11

          So, the result is: 33

        So, the result is: 3-3

      The result is: 2x32 x - 3

    The result of the chain rule is:

    5(2x3)(x23x)45 \cdot \left(2 x - 3\right) \left(x^{2} - 3 x\right)^{4}

  4. Now simplify:

    x4(x3)4(10x15)x^{4} \left(x - 3\right)^{4} \cdot \left(10 x - 15\right)


The answer is:

x4(x3)4(10x15)x^{4} \left(x - 3\right)^{4} \cdot \left(10 x - 15\right)

The graph
02468-8-6-4-2-1010-5000000000050000000000
The first derivative [src]
          4             
/ 2      \              
\x  - 3*x/ *(-15 + 10*x)
(10x15)(x23x)4\left(10 x - 15\right) \left(x^{2} - 3 x\right)^{4}
The second derivative [src]
    3         3 /            2             \
10*x *(-3 + x) *\2*(-3 + 2*x)  + x*(-3 + x)/
10x3(x3)3(x(x3)+2(2x3)2)10 x^{3} \left(x - 3\right)^{3} \left(x \left(x - 3\right) + 2 \left(2 x - 3\right)^{2}\right)
The third derivative [src]
    2         2            /          2               \
60*x *(-3 + x) *(-3 + 2*x)*\(-3 + 2*x)  + 2*x*(-3 + x)/
60x2(x3)2(2x3)(2x(x3)+(2x3)2)60 x^{2} \left(x - 3\right)^{2} \cdot \left(2 x - 3\right) \left(2 x \left(x - 3\right) + \left(2 x - 3\right)^{2}\right)
The graph
Derivative of (x^2-3x)^5