💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Like

Report

Numerade Educator

Like

Report

Problem 20 Medium Difficulty

Prove using the definition of derivative, that if $ f(x) = $ cos $ x, $ then $ f'(x) = - $ sin $ x. $

Answer

Check back soon!

More Answers

Discussion

You must be signed in to discuss.

Video Transcript

It's clear, so enumerated here. So we have the definition of the derivative. So are given is F of X is equal to co sign a X, then the derivative this equal to limit Does age approaches. Cerro Rico Signed Put X plus inch miners Co sign of X well over a tch. This gives us the limit. Thus each approaches Sarah Co Sign of X Times Coastline of H minus Sign of X times Sign of H minus Co sign of X over h excuse This limit Those age approaches Ciro her co sign Guns Co sign of age minus co Sign of X minus Sign of X times sign of H all over h And then this is Clement. That's H approaches Ciro for co sign of X Times Co sign of H minus one over H minus. Sign of X of sign of H over each. This gives us co sign of X times delimit as each approaches Ciro for co signed of H minus one over H minus sign of pecs for the limit as each approaches zero the sign of a TSH over change. So this becomes zero and this becomes one and this gives us a negative sign of X