Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

What is the derivative of the following function?

$$f(x)=(\sin^{3}(5x))^{\frac{1}{4}}$$

So I did the chain rule and I got

$$(\frac{1}{4})((\sin^{3}(5x))^{-3/4})(3\sin^2(5x))(\cos(5x))(5).$$

Does that look right? How do I simplify that? Thank you for the help and feedback!

share|improve this question
1  
Yes..it is correct! –  Tapu Feb 5 '13 at 18:41
    
awesome! how do I simplify that? That's where I seem to get stuck on these sorts of problems. –  user56852 Feb 5 '13 at 18:42
1  
$\sin^3(x)=(\sin x)^3$... –  Jp McCarthy Feb 5 '13 at 18:43
    
collect the exponents. will be some multiple of $\frac{\cos(5x)}{\sin^?(5x)}$ –  example Feb 5 '13 at 18:43
    
May be you first simplify your given function as $(\sin 5x)^\frac{3}{4}$..? –  Tapu Feb 5 '13 at 18:44
add comment

1 Answer

up vote 3 down vote accepted

As I said in the comment, you can do better by starting with $$(\sin 5x)^\frac{3}{4}$$

Then, its derivative w.r.t. $x$ is $$\frac{3}{4}(\sin 5x)^{-\frac{1}{4}}.\cos 5x. 5=\frac{15}{4}(\sin 5x)^{-\frac{1}{4}}.\cos 5x$$ Nothing simplifies more!

share|improve this answer
    
$\large{\frac{15}{2}(\sin 5x)^{-\frac{5}{4}}.\sin 10x}$ if you apply double angle rule...tops –  bryansis2010 Feb 5 '13 at 18:58
1  
Well,..then I must miss the meaning of simplify :) –  Tapu Feb 5 '13 at 19:01
    
applied $\large{\sin 2x = 2(\sin x)(\cos x)}$ –  bryansis2010 Feb 5 '13 at 19:03
    
thank you guys! –  user56852 Feb 5 '13 at 20:32
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.