Trouble with derivatives and fractions

[Silencher]

Hello, here's what I'm working on:

y = [(3x+2)^5]/[(5x+4)^3]


Step 1: Set g/h
g(x): (3x+2)^5
h(x): (5x+4)^3
g'(x): (3)(5)((3x+2)^4)
SIMPLIFIED: (15)((3x+2)^4)
h'(x): (5)(3)((5x+4)^2)
SIMPLIFIED: (15)((5x+4)^2)

Step 2: Plug into the quotient rule?

((45x+30)^5)(5x+4)^3) - ((75x+60)^2)((3x+2)^4) <--would that be correct?

 

[lookagain]

Hello, here's what I'm working on:

y = [(3x+2)^5]/[(5x+4)^3]


Step 1: Set g/h


g(x): (3x+2)^5 \(\displaystyle \ \ \ \) <------


h(x): (5x+4)^3 \(\displaystyle \ \ \ \) <------


g'(x): (3)(5)((3x+2)^4)


SIMPLIFIED: (15)((3x+2)^4) \(\displaystyle \ \ \ \) <------


h'(x): (5)(3)((5x+4)^2)


SIMPLIFIED: (15)((5x+4)^2) \(\displaystyle \ \ \ \) <------



Step 2: Plug into the quotient rule?

((45x+30)^5)(5x+4)^3) - ((75x+60)^2)((3x+2)^4) <--would that be correct?

\(\displaystyle Quotient \ \ Rule: \ \ \ \dfrac{[g(x)]*[f'(x)] \ - \ [f(x)]*[g'(x)]}{[g(x)]^2}\)



Why don't you try substituting the highlighted quantities into the quotient rule that I just typed?

 

[Silencher]

wrong

I tried that and it didn't work. I do have the correct answer, maybe you/someone can tell me where I went wrong? Something might also help might be a general formula for when I'm dealing with things like this, it seems like a combination of the chain rule and the quotient rule, but I'm not sure how to combine the formulas. Or if I even need to.



((45x+30)^5)(5x+4)^3) - ((75x+60)^2)((3x+2)^5) / (((5x+4)^3)^2)<---my answer [WRONG]


((3x+2)^4(30x+30))/((5x+4)^4)<----Right

 

[DrPhil]

I tried that and it didn't work. I do have the correct answer, maybe you/someone can tell me where I went wrong? Something might also help might be a general formula for when I'm dealing with things like this, it seems like a combination of the chain rule and the quotient rule, but I'm not sure how to combine the formulas. Or if I even need to.



((45x+30)^5)(5x+4)^3) - ((75x+60)^2)((3x+2)^5) / (((5x+4)^3)^2)<---my answer [WRONG]


((3x+2)^4(30x+30))/((5x+4)^4)<----Right

Your error was to move multipliers inside parentheses that are raised to a power. For instance, you can't take inside a 5th power unless you take the 5th root of 15. Try it again leaving the multipliers outside.