Module Question

Question

Find  by implicit differentiation for ycos(x) = xcos(y).

Answer 1

Use the product rule on both sides:

y(-sinx) + 1(cosx) dy/dx = x(-siny) dy/dx + 1(cosy)

-ysinx + cosx dy/dx = -xsiny dy/dx + cosy

Get the terms with dy/dx to one side and the terms without dy/dx to the other side:

cosx dy/dx + xsiny dy/dx = ysinx + cosy

Factor out dy/dx:

(cosx +xsiny) dy/dx = ysinx + cosy

Get dy/dx by itself:

dy/dx = (ysinx + cosy)/(cosx +xsiny)