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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

y = x (2 x + 3)

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

\frac{d}{d x} (ln (2 x y + 4))

\int e^{\frac{1}{2} x} d x

\int sec (t) (8 sec (t) + 7 tan (t)) d t

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