Solving for f'(x) using the chain and quotient rules

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Homework Statement



Let f(x) = (x2)/sin(x)2. Find f'(x).

Homework Equations



Chain rule, quotient rule

The Attempt at a Solution



f'(x) = [2xsin(x)2 - x22cos(x)2]/(sin(x)2)2
 
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char808 said:

Homework Statement



Let f(x) = (x2)/sin(x)2. Find f'(x).

Homework Equations



Chain rule, quotient rule

The Attempt at a Solution



f'(x) = [2xsin(x)2 - x22cos(x)2]/(sin(x)2)2

Derivative of sin(x)2 = cos(x)2*2x
 
f'(x) = [2xsin(x)2 - x22xcos(x)2]/(sin(x)2)2
 
BTW, the usual notation for (sin(x))2 is sin2(x).
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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