Question

find dy/dx if y=(3x+2)^(ln(x))

Answer 1

I've got ln(y) = ln(x)*ln(3x+2)

Answer 2

then i'm stuck

Answer 3

Then just use the product rule as normal.

Answer 4

you'll find that the derivative of lny= y'/y and since you just want y' in your final answer, just multiply both sides by y and plug in the y you originally started out with!

Answer 5

so, dy/dx (1/y) = (1/x)(ln 3x+2)+lnx(3/3x+2)
dy/dx = (y)(1/x)(ln 3x+2)+lnx(3/3x+2)

Answer 6

don't forget to multiply y times the second term as well and plug in your initial y (the function) from earlier so that everything is in terms of x.

Answer 7

dy/dx = (y) ((1/x)(ln 3x+2)+lnx(3/3x+2))

Answer 8

For your answer to be right, you must plug y back in, y=(3x+2)^(ln(x))