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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

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

\int 16 sin^{3} (x co) s^{2} x d x

\int sin (x t) d t

\frac{d}{d x} (x + y + z)

\int \frac{2 x ^{3} + 6 x ^{2} + 7 x + 4}{x ^{2} + 3 x + 2} d x

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