What is the derivative of sqrt(x^2-x+4) ?

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

What is the first derivative of sqrt(x^2-x+4) ?

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

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

\frac{2 x - 1}{2 x ^{2} - x + 4}

Solution steps

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

Apply the chain rule:

\frac{1}{2 x ^{2} - x + 4} \frac{d}{d x} (x^{2} - x + 4)

= \frac{1}{2 x ^{2} - x + 4} \frac{d}{d x} (x^{2} - x + 4)

\frac{d}{d x} (x^{2} - x + 4) = 2 x - 1

= \frac{1}{2 x ^{2} - x + 4} (2 x - 1)

Simplify

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

= \frac{2 x - 1}{2 x ^{2} - x + 4}

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