Question

e^2x +x³/cosec 2x differentiate with the help of x​

Answer 1

Answer:

d/dx(e^2x +x³/cosec 2x)

= d/dx(e^2x/cosec 2x) + d/dx(x³/cosec 2x)

= [cosec 2x {d/dx(e^2x)} - e^2x{d/dx(cosec 2x)}]/cosec^2(2x)

+ [ cosec 2x {d/dx(x³)} - x³{d/dx(cosec 2x)}]/cosec^2(2x)

= [2 e^2x cosec 2x  + cosec 2x cot 2x e^2x + 3x^2 cosec 2x + x^3 cosec 2x cot 2x]/cosec^2(2x)

= [e^2x ( 2 + cot 2x) + x^2 ( 3 + x cot 2x)]/cosec 2x