Saved Bookmarks
| 1. |
If y = ex^x then find dy/dx |
|
Answer» y = ex^x take log both sides, log y = loge ex^x log y = xx logee log y = xx (∵ log ee = 1) Again, taking log both sides, log(log y) = log xx log(log y) = x log x then differentiating w.r.t. x, = ((d log(log y))/d log y) x ((d log y)/dy) x (dy/dx) = (xd log x)/dx + (log x) x (dx/dx) = (1/log y) x (1/y) x (dy/dx) = (x) x (1/x) + log x = (1dy/(y log y dx)) - 1 + log x = dy/dx = (1 + log x)y log y = dy/dx =xx ex^x(1 + log x) |
|