my Think

Turunan fungsi Trigonometri
Pembuktian
Y = sin x dy/dx = cos x
Kalau y = sin x ……..(1)
y + Δy = sin(x + Δx) …….(2)
penyelesaian: (2) – (1)
y + Δy = sin (x + Δx)
y = sin x -
Δy = sin (x + Δx) – sin x
Δy/Δx=sin⁡〖((x + Δx))/Δx〗-sin⁡x
Δy/Δx= 〖sin x cos〗⁡〖Δx+cos⁡〖x sin⁡〖Δx-sin⁡x 〗 〗 〗/Δx
= (-sin⁡〖x +sin⁡〖x cos⁡〖Δx+cos⁡〖x sin⁡Δx 〗 〗 〗 〗)/Δx lim┬(Δx → 0) dy/dx =lim┬(Δx → 0) (- sin⁡〖x)〗 [lim┬(Δx → 0) (1-cos⁡∆x)/∆x] + [lim┬(Δx → 0)cos x] lim┬(Δx → 0) sin⁡x/∆x
dy/dx= -sin x .0 + cos x .1 = cos x
y = sin x → dy/dx = cos x

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