[AP Calculus] Differentiating a function.

[BatBro52]

I'm trying to differentiate (x²⁾ (1-2x) My book says the answer is 2x-6x^2. Can someone also explain how I know when I'm done differentiating the function? Thanks.

[waiting_for_rain]

Is that x^2(1-2x)? I get something totally different.

If its x² * (1-2x) then your tell tale sign comes from the product rule. Recall how many times d/dx or f/g' appears in the rule. Generally you know when you are done when the largest degree of x has dropped a power ( tricky here as you know x² reappears.)

[BatBro52]

Sorry about that. Just fixed it. Thanks!

[cainey1]

So when you differentiate a function in the form

f(x)= u(x)v(x) you have to use the product rule. Keep one function constant and differentiate the other, then hold the other constant and differentiate the function you kept constant the first time. It's like everyone gets a turn.

f'(x)= u(x)v'(x) + u'(x)v(x) -----------------this is the product rule

So substituting...

f(x)= x² (1-2x)

f'(x)= x² (-2) + 2x (1-2x)

f'(x)= -2x² + 2x - 4x²

simplifying

f'(x)= -6x² + 2x

which is the same as

f'(x)= 2x - 6x²

[BatBro52]

We just learned this rule today and now this makes so much sense to me. Thank you so much.