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
Related Maths A Level answers
All answers ▸Find the coordinates of the turning points of the curve y = 4/3 x^3 + 3x^2-4x+1
Sketch y = 9x – 4x^3, showing where the curve crosses the x axis.
Express 4sin(x)+6cos(x) in terms of Rsin(x+a) where R and a are constants to be determined (a should be given in rad).
At what point(s) do lines y = x^2 - 5x - 14 and y = 3x + 2 intersect? Write your answer in surd form