What is the derivative of sqrt(3x^2-4x+6) ?

The derivative of sqrt(3x^2-4x+6) is (3x-2)/(sqrt(3x^2-4x+6))

What is the first derivative of sqrt(3x^2-4x+6) ?

The first derivative of sqrt(3x^2-4x+6) is (3x-2)/(sqrt(3x^2-4x+6))

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\frac{d}{d x} (3 x^{2} - 4 x + 6)

\frac{3 x - 2}{3 x ^{2} - 4 x + 6}

Solution steps

\frac{d}{d x} (3 x^{2} - 4 x + 6)

Apply the chain rule:

\frac{1}{2 3 x ^{2} - 4 x + 6} \frac{d}{d x} (3 x^{2} - 4 x + 6)

= \frac{1}{2 3 x ^{2} - 4 x + 6} \frac{d}{d x} (3 x^{2} - 4 x + 6)

\frac{d}{d x} (3 x^{2} - 4 x + 6) = 6 x - 4

= \frac{1}{2 3 x ^{2} - 4 x + 6} (6 x - 4)

Simplify

\frac{1}{2 3 x ^{2} - 4 x + 6} (6 x - 4) : \frac{3 x - 2}{3 x ^{2} - 4 x + 6}

= \frac{3 x - 2}{3 x ^{2} - 4 x + 6}

What is the derivative of sqrt(3x^2-4x+6) ?
The derivative of sqrt(3x^2-4x+6) is (3x-2)/(sqrt(3x^2-4x+6))
What is the first derivative of sqrt(3x^2-4x+6) ?
The first derivative of sqrt(3x^2-4x+6) is (3x-2)/(sqrt(3x^2-4x+6))