Question

Find f'(x) if e^3x cosx. can someone help me solve. (:

Answer 1

It would be product rule correct because of the e^2x and the cosx.

Answer 2

*e^3x

Answer 3

Right, product rule. You know the derivative of e, right?

Answer 4

Derivative of e^x is e^x right? So I would set it up like this? \[e ^{3x}\times-sinx+cosx \times e^{3x}\times3 \]

Answer 5

Pfft, 0 ofc

Answer 6

Yeah, that looks fine to me. I always do it in a different order the books do it, though. I swear the books do it backwards, haha. But yes, thats fine.

Answer 7

Ahaha, thank you! Can I also ask another question?

Answer 8

u have to use the form of (u*v) in this ques
if u know the formula u can find out by differentiating

Answer 9

Did we do something wrong then mad?

Answer 10

i havent read ur comments..i jst gave my opinion

Answer 11

Oh, sorry. Thought you might have been correcting us, lol.

Answer 12

Find dy/dx if x=2 and \[y=\sqrt{2x-3}\] I would just make the radical to the power of 1/2 then do power rule right?

Answer 13

Right. And then be aware you have a chain rule since the derivative of the inside will make a difference.

Answer 14

\[\frac{ 1 }{ 2 }(2x-3)^{-1/2}\] I would get this after bringing down the 1/2 do I also need to multiply by the derivative of 2x-3 also?

Answer 15

Yes, you do. Technically, you are always multiplying by the derivatives of every inner layer, its just before you learn the chain rule officially, the derivatives of all the inner layers are 1 and they dont even point it out to you. So always assume you need the derivatives of the inner layers.

Answer 16

Alright thank you so much! I learned it and it was so simple but I suddenly blanked and forgot. I appreciate your help. (:

Answer 17

Yeah, absolutely.