What is the derivative of sqrt(3x^2+9x+2) ?

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

= \frac{1}{2 3 x ^{2} + 9 x + 2} \frac{d}{d x} (3 x^{2} + 9 x + 2)

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

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

Simplify

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

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

\frac{d y}{d x} = 0

\int \frac{e ^{x + 3}}{x + 3} d x

y = - \frac{1}{2} x^{2} + 2, y = 0

(y^{2} + 1) d x = y sec^{2} (x) d y

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