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Popular >

derivative of sqrt(x^2+x+3)

Solution

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

Solution

\frac{2 x + 1}{2 x ^{2} + x + 3}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{2 x + 1}{2 x ^{2} + x + 3}

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Frequently Asked Questions (FAQ)

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