
#1
May707, 08:56 AM

P: 101

How do you differentiate the likes of (sinx)^2
thanks 



#2
May707, 08:58 AM

Mentor
P: 8,287

Use the chain rule. Let u=sinx, then you need to find d/dx(u^2).




#3
May707, 09:05 AM

Emeritus
Sci Advisor
PF Gold
P: 9,789

Alternatively, you can recall / derive the power reduction formulae such as;
[tex]\sin^2\theta = \frac{1  \cos 2\theta}{2}[/tex] These are especially useful when integrating such functions. 



#5
May707, 05:06 PM

HW Helper
P: 3,353

I Think Hootenanny was in fact intended to use that to simplify the differentiation, if I'm reading his last sentence correctly >.<...Well anyway It doesn't really help very much because we still have to use the chain rule on the cos 2theta.




#6
May807, 03:33 AM

Emeritus
Sci Advisor
PF Gold
P: 9,789

[tex]\frac{d}{dx}\sin(ax) dx = a\cos(ax)[/tex] [tex]\int \sin(ax) dx = \frac{1}{a}\cos(ax) + C[/tex] Rather than remembering the results for the sin^{2}x etc. In any event applying the chain rule to something of the form sin(ax) is somewhat simpler than applying it to something of the form sin^{2}x don't you think? 



#7
May807, 03:39 AM

HW Helper
P: 3,353

Not always, usaully one would like an answer without double angled arguments, so they would have to know the expansion of cos(2theta) which isn't as easy as bringing a power down times the derivative of sin x.




#8
May807, 03:47 AM

Emeritus
Sci Advisor
PF Gold
P: 9,789





#9
May807, 04:29 AM

HW Helper
P: 3,353

Of course there all equivalent, but I always prefer putting my answers in terms in single angled arguments. In the end it makes very little difference, maybe 5 seconds working time.




#10
May807, 10:50 AM

P: 15

= 2sinx cosx
= sin2x 



#11
May907, 05:59 PM

P: 2

w00t 1st post :P 



#12
May907, 06:08 PM

Mentor
P: 4,499

Let's try not to get into a 12 page debate on the merits of single vs. double angle final form solutions



Register to reply 
Related Discussions  
How do I differentiate  Calculus  3  
Differentiate the Following  Calculus & Beyond Homework  1  
how do you differentiate this  Calculus & Beyond Homework  5  
differentiate this, i need help  Calculus & Beyond Homework  4  
differentiate  Calculus & Beyond Homework  6 