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Popular >

derivative of sqrt(x^2+6x+3)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

derivative of 3x^2-12x+9

\frac{d}{d x} (3 x^{2} - 12 x + 9)

11t^2y^{''}-22y=9t^2-9

11 t^{2} y^{^{''}} - 22 y = 9 t^{2} - 9

limit as x approaches 0 of cos(2-2e^x)

x \to 0 lim (cos (2 - 2 e^{x}))

limit as x approaches 1 of 2

x \to 1 lim (2)

limit as x approaches 6-of tan((pix)/4)

x \to 6 - lim (tan (\frac{π x}{4}))

Frequently Asked Questions (FAQ)

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