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Jiaxuan
Meaning of implicit differentiation
Functions can be of two types.. (remember a simple non technical def of function is how a variable y changes with some variable x.. so its like you keep changing x, and you wanna see what happens to y, we say y is function of x) if i denote this function this way y = 3x + 5 then.. what i have done is EXPLICITLY defined the function y.. (its like i cannot make it ANY MORE CLEAR WHAT y is.. we even use this.. we say "I EXPLICITLY TOLD YOU not to run away from house didn't i??) now instead imagine you have a function 3y + x = 5sin(xy) look at this bad boy function.. if you ask yourself.. hmm what is y?.. you dunno exactly cause its EXPLICITLY not defined.. we call this as an implicit function