myrmepropagandist on Nostr: Calculus Question: First you use the limit definition of f'(x) and find f'(x) this ...
Calculus Question:
First you use the limit definition of f'(x) and find f'(x) this gets more and more messy. Then you prove the power/quotient/product/chain rules and use them instead.
No one ever uses the limit definition for something like f(x)=[x-sqrt(x-3)]/[x^4-x^2-5]
You'd fill pages expanding (x+h) to various powers and clearing roots.
But are there any functions that *can't* be algebra'd to their typical form using the rules? I assume not.
Worst case the limit itself is f'(x).
First you use the limit definition of f'(x) and find f'(x) this gets more and more messy. Then you prove the power/quotient/product/chain rules and use them instead.
No one ever uses the limit definition for something like f(x)=[x-sqrt(x-3)]/[x^4-x^2-5]
You'd fill pages expanding (x+h) to various powers and clearing roots.
But are there any functions that *can't* be algebra'd to their typical form using the rules? I assume not.
Worst case the limit itself is f'(x).