What is the derivative of sqrt(x^2+6x+9) ?

The derivative of sqrt(x^2+6x+9) is (x+3)/(sqrt(x^2+6x+9))

What is the first derivative of sqrt(x^2+6x+9) ?

The first derivative of sqrt(x^2+6x+9) is (x+3)/(sqrt(x^2+6x+9))

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derivative of

x^{2} + 6 x + 9

\frac{x + 3}{x ^{2} + 6 x + 9}

Solution steps

\frac{d}{d x} (x^{2} + 6 x + 9)

Apply the chain rule:

\frac{1}{2 x ^{2} + 6 x + 9} \frac{d}{d x} (x^{2} + 6 x + 9)

= \frac{1}{2 x ^{2} + 6 x + 9} \frac{d}{d x} (x^{2} + 6 x + 9)

\frac{d}{d x} (x^{2} + 6 x + 9) = 2 x + 6

= \frac{1}{2 x ^{2} + 6 x + 9} (2 x + 6)

Simplify

\frac{1}{2 x ^{2} + 6 x + 9} (2 x + 6) : \frac{x + 3}{x ^{2} + 6 x + 9}

= \frac{x + 3}{x ^{2} + 6 x + 9}

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What is the derivative of sqrt(x^2+6x+9) ?
The derivative of sqrt(x^2+6x+9) is (x+3)/(sqrt(x^2+6x+9))
What is the first derivative of sqrt(x^2+6x+9) ?
The first derivative of sqrt(x^2+6x+9) is (x+3)/(sqrt(x^2+6x+9))