Find 𝑑^2𝑥/𝑑𝑥^2 by implicit differentiation 𝑦^2 + 𝑥^2 = 𝑒 √sin 𝑥𝑦+ln 𝑥𝑦

Answer 1

Implicit Differentiation, Just apply d/dx in place for all terms and remember to use chain rule when applying d/dx to functions of y. You can then solve for dy/dx by grouping and isolating:

In order to find second derivative, you must take d/dx of dy/dx expression

I can't work out the 3rd term from the way you wrote it, but I'll show other terms:

2yy' + 2x = ? + 1/(xy) *(y + xy')