Expert: Paul Klarreich - 5/2/2009

Question
1.how do I do, find f'(x)
f(x)=4xsinxcosx


2. how do I find f'(x) of f(x)=2secx+2(e^x)tanx

and also

3. f(x)=(4x^2-1x+4)e^x... find f'(x)


I don't understand using e^x and I thought I was just suppose to find the deriv of cosx by swtiching it to -sinx and sinx to cosx. but thats not right. please HELP!


Answer
Questioner:   ray
Country:  United States
Category:  Calculus
Private:  No
 
Subject:  derivatives
Question:  1.how do I do, find f'(x)
f(x)=4xsinxcosx


2. how do I find f'(x) of f(x)=2secx+2(e^x)tanx

and also

3. f(x)=(4x^2-1x+4)e^x... find f'(x)


I don't understand using e^x and I thought I was just suppose to find the deriv of cosx by switching it to -sinx and sinx to cosx. but thats not right. please HELP!
............................................
Hi, Ray,

It sounds like you are learning the product rule.

If f(x) = 4x sin x cos x

then this is a product:
First function: x sin x  << we'll just carry through the factor of 4
Second function:  cos x

f'(x) = 4[(x sin x)(-sin x) + (cos x)(D(x sin x)) ]

and the derivative of x sin x is another product rule thing:

D(x sin x) = (x)(cos x) + (sin x)(1)

Now put it all together.

............................................

Your others are just product rule applications(mostly) and you will just have to wait until your teacher covers the derivative of e^x.

Note: You do NOT find a derivative by 'switching'.  Learn the vocabulary of mathematics and use it correctly or you will surely fail.