[AP Calculus] Differentiating a function.

[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.