What is the derivative of f(x)= 1/(3(x)^2+2(x)) ?

The derivative of f(x)= 1/(3(x)^2+2(x)) is -(6x+2)/((3x^2+2x)^2)

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

The first derivative of f(x)= 1/(3(x)^2+2(x)) is -(6x+2)/((3x^2+2x)^2)

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derivative of

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

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

f (x) = 2 x^{3} + 42 x^{2} + 288 x + 14

y = 2 - 6 x

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

f (x) = - x^{2}

x \to 7 lim (\frac{3}{x - 7})

What is the derivative of f(x)= 1/(3(x)^2+2(x)) ?
The derivative of f(x)= 1/(3(x)^2+2(x)) is -(6x+2)/((3x^2+2x)^2)
What is the first derivative of f(x)= 1/(3(x)^2+2(x)) ?
The first derivative of f(x)= 1/(3(x)^2+2(x)) is -(6x+2)/((3x^2+2x)^2)