Mister Exam

Derivative of (x-1)^5

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

The graph:

from to

Piecewise:

The solution

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       5
(x - 1) 
(x1)5\left(x - 1\right)^{5}
d /       5\
--\(x - 1) /
dx          
ddx(x1)5\frac{d}{d x} \left(x - 1\right)^{5}
Detail solution
  1. Let u=x1u = x - 1.

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

  3. Then, apply the chain rule. Multiply by ddx(x1)\frac{d}{d x} \left(x - 1\right):

    1. Differentiate x1x - 1 term by term:

      1. Apply the power rule: xx goes to 11

      2. The derivative of the constant (1)1\left(-1\right) 1 is zero.

      The result is: 11

    The result of the chain rule is:

    5(x1)45 \left(x - 1\right)^{4}

  4. Now simplify:

    5(x1)45 \left(x - 1\right)^{4}


The answer is:

5(x1)45 \left(x - 1\right)^{4}

The graph
02468-8-6-4-2-1010-250000250000
The first derivative [src]
         4
5*(x - 1) 
5(x1)45 \left(x - 1\right)^{4}
The second derivative [src]
           3
20*(-1 + x) 
20(x1)320 \left(x - 1\right)^{3}
The third derivative [src]
           2
60*(-1 + x) 
60(x1)260 \left(x - 1\right)^{2}
The graph
Derivative of (x-1)^5