Differentiate y=x/sin(x)
This equation has one function of x divided by another function of x, we therefore have to use the quotient rule and is written in the form f(x)/g(x).
The quotient rule is therefore
f'(x)g(x)-g'(x)f(x)/g2(x)
The first step would be to differentiate f(x) and g(x).
f'(x)=1 g'(x)=cos(x)
The numerator of this fraction would therefore be
1*sin(x)-xcos(x) =sin(x)-xcos(x)
To calculate the denominator you simply square g(x)
g2(x)= sin2(x)
So the answer would be sin(x)-xcos(x)/sin2(x)
RF
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