Question
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.
Answers
Reiny
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
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
Raj
Why can't we do this for questions like f(X)=15/(2x+1)^1/3
Reiny
We can!
dy/dx = (1/3)(15)(2x+1)^(1/3 -1) * 2
= 10(2x+1)^(-2/3) , done in 2 steps!
dy/dx = (1/3)(15)(2x+1)^(1/3 -1) * 2
= 10(2x+1)^(-2/3) , done in 2 steps!