How do you differentiate cosx?
Differentiate cos x using the first principle of derivatives :
ddx(cosx)=limh→0[cos(x+h)–cosx]hlimh→0[f(x+h)–f(x)]h=limh→0[cosxcosh–sinxsinh–cosx]h=limh→0cosx[(cosh–1)]h-sinx(sinh)h=0–sinxlimx→0sinxx=1=-sinx
Hence ,the differentiation of cosx is -sinx.