Optimization: If A=3x2y and y= (25-2x)^5 show that dA/dx= 6x(25-2x)^4(25-7x)

[5paghetti]

"If A=3x²y and y= (25-2x)^5 show that dA/dx= 6x(25-2x)^4(25-7x)
Hence determine the values of x for which A has stationary points and use either the second derivative test or the sign test, whichever you consider the more appropriate, to determine the nature of each."

Working ahead in class and came across this question. I'm not sure how I should approach finding the derivative. I've tried using the product and chain rule together but I'm not getting anything near what I should be. Any help with this would be much appreciated.

 

[Ishuda]

"If A=3x²y and y= (25-2x)^5 show that dA/dx= 6x(25-2x)^4(25-7x)
Hence determine the values of x for which A has stationary points and use either the second derivative test or the sign test, whichever you consider the more appropriate, to determine the nature of each."

Working ahead in class and came across this question. I'm not sure how I should approach finding the derivative. I've tried using the product and chain rule together but I'm not getting anything near what I should be. Any help with this would be much appreciated.

What are your thoughts? What have you done so far? Please show us your work even if you feel that it is wrong so we may try to help you. You might also read
http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting

Hint: let G(x) = f(y₁(x)) h(y₂(x)), then
G' = (df/dy₁) (dy₁/dx) h(y₂(x)) + f(y₁(x)) (dh/dy₂) (dy₂/dx)

 

[stapel]

"If A=3x²y and y= (25-2x)^5 show that dA/dx= 6x(25-2x)^4(25-7x)..."

...I've tried using the product and chain rule together but I'm not getting anything near what I should be.

Please reply with a clear listing of what you've tried so far, so we can see where things are going sideways. Thank you!