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Derivative of:
Derivative of -sin2x
Derivative of log(x+3)^3
Derivative of cos(3*x)^(2)
Derivative of 2/x^4
Integral of d{x}:
(x-1)^5
Canonical form:
(x-1)^5
Graphing y =:
(x-1)^5
Identical expressions
(x- one)^ five
(x minus 1) to the power of 5
(x minus one) to the power of five
(x-1)5
x-15
(x-1)⁵
x-1^5
Similar expressions
y=(√x^2+7x)^3-(√4x-1)^5
(x+1)^5

The derivative of the function/ (x-1)^5

Derivative of (x-1)^5

The solution

You have entered [src]

       5
(x - 1)

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

d /       5\
--\(x - 1) /
dx

\frac{d}{d x} \left(x - 1\right)^{5}

Transform

Detail solution

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

$5 \left(x - 1\right)^{4}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

         4
5*(x - 1)

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

Simplify

The second derivative [src]

           3
20*(-1 + x)

20 \left(x - 1\right)^{3}

Simplify

The third derivative [src]

           2
60*(-1 + x)

60 \left(x - 1\right)^{2}

Simplify

The graph

Derivative of (x-1)^5