Question

Hey everyone, Could someone help me on this question please,

Find the derivative of -y^3(3xy^2+5)^-1

I'm just really confused on the (3xy) part, thanks
.

Answer 1

Would I use the chain rule and then product rule for the 3xy?

Answer 2

yes...

Answer 3

I tried that but I it seems i'm doing a mistake, how would I include the product rule within another rule?

Answer 4

if u are finding problem with that part then try considering the product of xy as another variable and then find the derivative of the y^(expr) part...

Answer 5

i mean find the expr part derivative first, keep it aside and then solve it total in the form of y^x and then multiply with the obtained derivative..

Answer 6

Oh, so basically I do the chain rule for the whole thing, and then when it asks for the derivate of 3xy^2+5 I use the product rule ? Thanks for the help so far.

Answer 7

yes... im solving it... wait.. i will give u the answer..

Answer 8

Thanks a lot, can you show me some steps as well?

Answer 9

ok..

Answer 10

-(3(y^2)(3xy^2+5)/2x)log y

Answer 11

the above method takes a lot of time... prob is about 2 pages. So solve it by using implicit function method... d/dx(f(x,y))=-(partial df/dx)/(partial df/dy)
this solves the problem in a simpler way... i got the answer as given above..

Answer 12

Ohh okay, thanks a lot for your help, I appreciate it.