Question

Using quotient rule, differentiable with respect to x

(i) y = (x⁵ - cosx)/sinx

(ii) y = (x + cosx)/tanx

(iii) y = cosx/(1 + sinx)

Answer 1

(i) dy/dx = (sinx(5x + sinx) - (x⁵ - cosx)cosx)/sin²x

(ii) dy/dx = (tanx(1 - sinx) - (x + cosx)sec²x)/tan²x