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Numerade Educator



Problem 20 Medium Difficulty

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


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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