I have just come across implicit differentiation in my study of calculus and I am slightly confused. Why do I have to use the chain rule to differentiate a function implicitly? More importantly, why CAN'T I use the simple power rule?
Yes, I understand that. That is the rule stated in my textbook, but I don't understand why it is true. It seems arbitrary. WHY do we use the chain rule when "the function is not explicitly in terms of the variable in question," rather than the simple power rule?
A function not explicitly (but implicitly) in terms of x is a function of a function of x, i.e. a composite function of x.
And when do we ever use the chain rule?
Btw... don't integrate - balloontegrate!
... though, in this case, I should say, don't differeniate - balloontiate! E.g., the chain rule...
Balloon Calculus; standard integrals, derivatives and methods
I understand that a function can be defined implicitly in terms of x, but can someone please explain to me why I can't use the simple power rule to implicitly differentiate? Please can someone explain this to me; this is so frustrating. Maybe I should clear up my question a little bit: why is: d/dx [ył2] = 2y* dy/dx and not just 2y.
Thank you skeeter. That was definitely the most helpful reply, but I just have one more question. Is there anything in the definition of the simple power rule that suggests you can't use it when implicitly differentiating a function?