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Popular >

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

Solution

derivative of

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

Solution

\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}

Popular Examples

derivative of (x^3/3+c)

\frac{d}{d x} (\frac{x ^{3}}{3} + c)

limit as x approaches 5 of (x^3+8)/(x+2)

x \to 5 lim (\frac{x ^{3} + 8}{x + 2})

derivative of x-1/(1+x)

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

integral of ((x+4))/(x^2+2x+5)

\int \frac{( x + 4 )}{x ^{2} + 2 x + 5} d x

inverse oflaplace s/((s^2+25)(s-1))inverse laplace

\frac{s}{( s ^{2} + 25 ) ( s - 1 )}

Frequently Asked Questions (FAQ)

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))