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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

derivative of x^{3/2}-4

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

derivative of (sqrt(x)/(x+6))

\frac{d}{d x} (\frac{x}{x + 6})

integral from 3 to 6 of 21-(x^2)/2

\int_{3}^{6} 21 - \frac{x ^{2}}{2} d x

integral of 1/(sqrt(7-x^2))

\int \frac{1}{7 - x ^{2}} d x

integral from 0 to 2 of (x-2)/(x-1)

\int_{0}^{2} \frac{x - 2}{x - 1} d x

Frequently Asked Questions (FAQ)

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