Find the derivative. Please help!! f(x)=-3x[(-6)/(x+2)]

Question

callisto · Answer

$$f(x) = -3x(\frac{-6}{x+2})$$ Is this f(x) you've typed?

smurfy14 · Answer

there should be a minus sign after -3x. sorry

callisto · Answer

$$f(x) = -3x - \frac{-6}{x+2}$$ This?

smurfy14 · Answer

ya

callisto · Answer

$$f(x) = -3x - \frac{-6}{x+2}$$$$f'(x) = \frac{d}{dx}(-3x) - \frac{d}{dx} (\frac{-6}{x+2})$$$$f'(x) = -3 - (-6)\frac{d}{dx} (\frac{1}{x+2})$$$$f'(x) = -3 +(6)\frac{d}{dx} (\frac{1}{x+2})$$$$f'(x) = -3 +(6)(-1) (\frac{1}{(x+2)^2})$$$$f'(x) = -3 -6 (\frac{1}{(x+2)^2})$$$$f'(x) = -3 - \frac{6}{(x+2)^2}$$

smurfy14 · Answer

what does d/dx mean?

callisto · Answer

Differentiate (something) with respect to x ...

smurfy14 · Answer

i dont know how you got rid of the x from -3x between lines 2 and 3

callisto · Answer

$$\frac{d}{dx} ax^n = anx^{n-1}$$
Now, n =1, a=-3 
$$\frac{d}{dx} -3x^1 = (-3)(1)x^{1-1} = -3$$
Note that $$x^0 =1$$

smurfy14 · Answer

oh ok i get it! one more questuon, why isnt the (x+2)^2 under the -3 as well?

callisto · Answer

They are two terms...

smurfy14 · Answer

ok i got it thanks a bunch!!

callisto · Answer

Welcome!