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

The derivative of f(x)=(x-1)sqrt(x^2-2x+2) is (2x^2-4x+3)/(sqrt(x^2-2x+2))

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

The first derivative of f(x)=(x-1)sqrt(x^2-2x+2) is (2x^2-4x+3)/(sqrt(x^2-2x+2))

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derivative of

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

\frac{2 x ^{2} - 4 x + 3}{x ^{2} - 2 x + 2}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x - 1, g = x^{2} - 2 x + 2

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

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

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

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

Simplify

1 \cdot x^{2} - 2 x + 2 + \frac{x - 1}{x ^{2} - 2 x + 2} (x - 1) : \frac{2 x ^{2} - 4 x + 3}{x ^{2} - 2 x + 2}

= \frac{2 x ^{2} - 4 x + 3}{x ^{2} - 2 x + 2}

\int x^{5} e^{x^{3} - 7} d x

n = 1 \sum \infty \frac{3}{4 n ^{2} - 1}

1 + cos (2 x)

\frac{\partial}{\partial x} (\frac{100 x}{( x + y ) ^{2}})

\int 10 e^{- 2 x} d x

What is the derivative of f(x)=(x-1)sqrt(x^2-2x+2) ?
The derivative of f(x)=(x-1)sqrt(x^2-2x+2) is (2x^2-4x+3)/(sqrt(x^2-2x+2))
What is the first derivative of f(x)=(x-1)sqrt(x^2-2x+2) ?
The first derivative of f(x)=(x-1)sqrt(x^2-2x+2) is (2x^2-4x+3)/(sqrt(x^2-2x+2))