Differentiate the following functions with respect to x :
ex−tan xcot x−xn
Using quotient rule, we have,
ddx(ex−tan xcot x−xn)
=(cot x−xn)ddx(ex−tan x)−(ex−tan x)ddx(cot x−xn)(cot x−xn)2
=(cot x−xn)(ex−sec2x)−(ex−tan x)(−cosec2x−nxn−1)(cot x−xn)2
=(cot x−xn)(ex−sec2x)+(ex−tan x)(cosec2x+nxn−1)(cot x−xn)2