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Popular >

derivative of sqrt(x^2+2x+8)

Solution

\frac{d}{d x} (x^{2} + 2 x + 8)

Solution

\frac{x + 1}{x ^{2} + 2 x + 8}

Solution steps

\frac{d}{d x} (x^{2} + 2 x + 8)

Apply the chain rule:

\frac{1}{2 x ^{2} + 2 x + 8} \frac{d}{d x} (x^{2} + 2 x + 8)

= \frac{1}{2 x ^{2} + 2 x + 8} \frac{d}{d x} (x^{2} + 2 x + 8)

\frac{d}{d x} (x^{2} + 2 x + 8) = 2 x + 2

= \frac{1}{2 x ^{2} + 2 x + 8} (2 x + 2)

Simplify

\frac{1}{2 x ^{2} + 2 x + 8} (2 x + 2) : \frac{x + 1}{x ^{2} + 2 x + 8}

= \frac{x + 1}{x ^{2} + 2 x + 8}

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Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x^2+2x+8) ?
The derivative of sqrt(x^2+2x+8) is (x+1)/(sqrt(x^2+2x+8))
What is the first derivative of sqrt(x^2+2x+8) ?
The first derivative of sqrt(x^2+2x+8) is (x+1)/(sqrt(x^2+2x+8))