Can we write derivative of 5(2x-3)^-3 directly 5*-3(2x-3)^-3-1 *coefficient of x, instead of using chain rule.In what type of question this is applicable and in which question not?Please explain.

Answer 1

Don't say "instead of using the chain rule", since the result you stated comes from the chain rule
I given y = 5(2x-3)^-3 I would write the derivative as
dy/dx = -15(2x-3)^-3 * 2 = -30(2x-3)^-4

The detailed steps would only be done when you first learn how the process works. Once you have mastered the procedure, you can state the answer directly in usually 2 steps

e.g y = 3(3x^3 - 7)^7
dy/dx = 21(3x^3 - 7)^6 * 9x^2
= 189x^2(3x^3-7)^6

Answer 2

Why can't we do this for questions like f(X)=15/(2x+1)^1/3

Answer 3

We can!

dy/dx = (1/3)(15)(2x+1)^(1/3 -1) * 2
= 10(2x+1)^(-2/3) , done in 2 steps!