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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)

Rowan F. A Level Chemistry tutor, GCSE Biology tutor, GCSE Chemistry ...

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