Question

How do you differentiate `f(x)= (2 x^2 + 7 x - 2)/ (x sinx )` using the quotient rule?

Answer 1

The Quotient Rule says `d/dx(f(x)/g(x))=(g(x) * f'(x) - f(x) * g'(x))/((g(x))^2)`. This, in addition to the product rule, linearity, and the power rule, gives:

`d/dx((2x^2+7x-2)/(x sin(x)))=(x sin(x) * (4x+7) - (2x^2+7x-2) * (sin(x) + x cos(x)))/(x^2 sin^{2}(x))`

`=(2x^{2}sin(x)+2sin(x)-2x^{3}cos(x)-7x^{2}cos(x)+2xcos(x))/(x^2 sin^{2}(x))`