High School Calculus/Implicit Differentiation

Implicit Differentiation When a functional relation between x and y cannot be readily solved for y, the preceding rules may be applied directly to the implicit function. The derivative will usually contain both x and y. Thus the derivative of an algebraic function, defined by setting the polynomial of x and y to zero. Ex. 1 Given the function y of x Find Since In solving for we must first factor the differentiation problem In doing this we get From here we subtract the to one side Thus giving us Here I am going to skip a step in solving this implicit differentiation problem. I am going to skip the step where I divide the -1 over to the other side. From here we divide the polynomial from the over to the other side. Giving us Now we simplify and get Other problems to work on Ex. 2 Find given the function Ex. 3 Find given the function