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Popular Calculus >

derivative of sqrt(3x^2+9x+2)

Solution

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

Solution

\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}

Graph

Popular Examples

integral of (e^{sqrt(x+3)})/(sqrt(x+3))

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

area y=-1/2 x^2+2,y=0

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

integral of \sqrt[9]{e^x}

\int 9 e^{x} d x

(y^2+1)dx=ysec^2(x)dy

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

limit as x approaches 0 of x^{-2}

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

Frequently Asked Questions (FAQ)

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))