MATH 1A Lecture Notes - Lecture 16: Power Rule, Pythagorean Theorem, Hypotenuse
Document Summary
Math 1a lecture 16 3. 5 implicit differentiation (contd. ) and 3. 6 differentiation of. Application of implicit differentiation: finding derivatives of inverse functions f (f 1( y))= y and f 1( f ( x))=x . Recall, if y=f (x) is one-to-one on some interval, then an inverse function x=f 1( y) exists on that interval, such that. The inverse is x=f 1( y)= 3 y. Q: find the derivative of y=f 1( x) A: if y=f 1( x) starting with x=f ( y) , and implicit differentiation allows us to find. , by differentiating both sides with respect to x . dy dx , x=f ( y) f ( y) d dx. 1= d dy x= d dx f ( y ) y =f 1 ( x) d dx y (think of y as a function of x . The same function we started with, i. e. y=f 1( x)
