Chain rule :
dy/dx = du/dx * dy/du
I think I can get the answers right but I'm having trouble simplifying.
Q1. Find derivative for y = 1/10 * (1 - 3x ^4) ^5 (by using chain rule) (I leave a space between base and power... e.g [7 ^5])
I got: 1/2 (1 - 3x ^4) ^4 * -(12x ^3). I think this is correct but the answers show -6x ^3 (3x ^4 - 1)
When I simplified: 1/2 * -(12x ^3) = -6x ^3, therefore I derived -6x ^3(1 - 3x ^4) ^4 !?
Q2. I was wondering what steps must be taken in a situation like so: (8+12) ^2. Might sound silly, but If I want to take common factor out from brackets (4), how do I do this? I think you must square the common factor outside of brackets, but what is the rule? I think I haven't come across something like that before, not until I came across a derivative question with this concept involved.
Q3. Find derivative using chain rule.
y = -1 / (1 + 1/x)
Think I got it right, but simplifying was a problem. The textbook had : -1 / (x + 1) ^2
Please explain all steps, I'm really confused.
dy/dx = du/dx * dy/du
I think I can get the answers right but I'm having trouble simplifying.
Q1. Find derivative for y = 1/10 * (1 - 3x ^4) ^5 (by using chain rule) (I leave a space between base and power... e.g [7 ^5])
I got: 1/2 (1 - 3x ^4) ^4 * -(12x ^3). I think this is correct but the answers show -6x ^3 (3x ^4 - 1)
When I simplified: 1/2 * -(12x ^3) = -6x ^3, therefore I derived -6x ^3(1 - 3x ^4) ^4 !?
Q2. I was wondering what steps must be taken in a situation like so: (8+12) ^2. Might sound silly, but If I want to take common factor out from brackets (4), how do I do this? I think you must square the common factor outside of brackets, but what is the rule? I think I haven't come across something like that before, not until I came across a derivative question with this concept involved.
Q3. Find derivative using chain rule.
y = -1 / (1 + 1/x)
Think I got it right, but simplifying was a problem. The textbook had : -1 / (x + 1) ^2
Please explain all steps, I'm really confused.