Tentukan turunan dari fungsi f(x) berikut f(x)=cotx

Halo Luna S :) Jawaban: f'(x) = - cosec^2 x perhatikan bahwa: cot x = 1/tan x sec x = 1/cos x cosec x = 1/sin x tan x = sin x / cos x jika f(x) = (tan x)^a, maka turunannya: f'(x) = [a][(sec x)^2][(tan x)^(a-1)] sehingga dapat dihitung: f(x) = cot x f(x) = 1/tan x f(x) = (tan x)^(-1) turunannya: f(x) = (tan x)^(-1) f'(x) = [-1][(sec x)^2][(tan x)^(-1-1)] f'(x) = [-1][(sec x)^2][(tan x)^(-2)] f'(x) = [-(sec x)(sec x)]/[(tan x)(tan x)] karena sec x = 1/cos x; dan tan x = sin x / cos x f'(x) = [-(sec x)(sec x)]/[(tan x)(tan x)] f'(x) = [-(1/cos x)(1/cos x)]/[(sin x/cos x)(sin x/cos x)] f'(x) = [-1/(cos x)^2]/[(sin x)^2 / (cos x)^2] f'(x) = [-1/(cos x)^2] . [(cos x)^2 / (sin x)^2] f'(x) = [-1/(sin x)^2] f'(x) = -[1/(sin x)][1/(sin x)] f'(x) = -[1/(sin x)][1/(sin x)] karena cosec x = 1/sin x f'(x) = -[1/(sin x)][1/(sin x)] f'(x) = -[cosec x][cosec x] f'(x) = -(cosec x)^2 f'(x) = - cosec^2 x Jadi, turunan dari fungsi f(x)=cotx adalah... f'(x) = - cosec^2 x terima kasih