How do you find the derivative of f(x)= 1/(9x+6)^2f(x)=1(9x+6)2?

1 Answer
Feb 22, 2016

f'(x) = -2 / (3*(3x + 2)^{3})

Explanation:

Since this is under the chain rule, then use it.

Substitute u = 9x + 6.

frac{"d"u}{"d"x} = 9

So plug it in.

f'(x) = frac{"d"}{"d"x}(1/(9x + 6)^2)

= frac{"d"}{"d"x}(1/u^2)

= frac{"d"}{"d"u}(u^{-2})*frac{"d"u}{"d"x}

= (-2) * u^{-3} * (9)

= -18 / (9x + 6)^{3}

= -18 / (3^3*(3x + 2)^{3})

= -2 / (3*(3x + 2)^{3})