What is the derivative of f(x)=sqrt(x^2-2x+1) ?

The derivative of f(x)=sqrt(x^2-2x+1) is (x-1)/(sqrt(x^2-2x+1))

What is the first derivative of f(x)=sqrt(x^2-2x+1) ?

The first derivative of f(x)=sqrt(x^2-2x+1) is (x-1)/(sqrt(x^2-2x+1))

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derivative of

f (x) = x^{2} - 2 x + 1

\frac{x - 1}{x ^{2} - 2 x + 1}

Solution steps

\frac{d}{d x} (x^{2} - 2 x + 1)

Apply the chain rule:

\frac{1}{2 x ^{2} - 2 x + 1} \frac{d}{d x} (x^{2} - 2 x + 1)

= \frac{1}{2 x ^{2} - 2 x + 1} \frac{d}{d x} (x^{2} - 2 x + 1)

\frac{d}{d x} (x^{2} - 2 x + 1) = 2 x - 2

= \frac{1}{2 x ^{2} - 2 x + 1} (2 x - 2)

Simplify

\frac{1}{2 x ^{2} - 2 x + 1} (2 x - 2) : \frac{x - 1}{x ^{2} - 2 x + 1}

= \frac{x - 1}{x ^{2} - 2 x + 1}

What is the derivative of f(x)=sqrt(x^2-2x+1) ?
The derivative of f(x)=sqrt(x^2-2x+1) is (x-1)/(sqrt(x^2-2x+1))
What is the first derivative of f(x)=sqrt(x^2-2x+1) ?
The first derivative of f(x)=sqrt(x^2-2x+1) is (x-1)/(sqrt(x^2-2x+1))