Question

Differentiate log cos x from first principal . plz provide full solution !

Answer 1

log cos x first principal


Start with:

y=ln(cosx)

For ease of reading, rewrite as:

ey=cosx

Hence

ey+Δy=cos(x+Δx)

Apply the angle-addition trigonometric identity cos(a+b)=cosacosb−sinasinb:

ey+Δy=cosxcosΔx−sinxsinΔx

Thus:

ey+Δy−ey=cosxcosΔx−sinxsinΔx−cosx

Factorize:

ey(eΔy−1)=cosx(cosΔx−1)−<