<|begin_of_text|><|start_header_id|>system<|end_header_id|>

You are a helpful chatbot that always answers in Uzbek.<|eot_id|><|start_header_id|>user<|end_header_id|>

Iltimos, LaTeX yordamida yozilgan matematik funksiya hosilasini bosqichma-bosqich hisoblang: `$\frac{1}{2\sin^2{(2x-4\ln5)}}$`<|eot_id|><|start_header_id|>assistant<|end_header_id|>

Ushbu funksiyaning cheklangan hosilasi quyidagicha: $\frac{d}{dx}\left(\frac{1}{2\sin^2{(2x-4\ln5)}}\right) = -\frac{4\cos{(2x-4\ln5)}}{2\sin^3{(2x-4\ln5)}}$ Ushbu funksiyaning hosilasini hisoblash uchun biz quyidagi qadamlardan foydalanishimiz mumkin: Biz teskari funksiyaning differensiallash qoidasini qo'llaymiz: $\frac{d}{dx}\sin^-1}{u} = \frac{1}{sqrt{1-u^2}}\c{\frac{du}{dx}{d}{d}{2}{{d}{{f}{{{d}}}{d}{d}<|eot_id|><|start_header_id|>user<|end_header_id|>

Endi esa, shu funksiya bilan ikkinchi hosilani toping.<|eot_id|><|start_header_id|>assistant<|end_header_id|>

Ushbu funksiya ikkinchi hosilasini hisoblash uchun birinchi hosilasi differensiallashtiriladi. Avval birinchi hosilasi topamiz: $$f'(x) = -\frac{4\cos{(2x - 4\ln5)}}{2\sin^3{(2x - 4\ln5)}} = -\frac{2\cos{(2x - 4\ln5)}}{\sin^3{(2x - 4\ln5)}}$$ Endi birinchi hosilasi differensiallashtiriladi: $$f'(x) = \frac{d}{dx} \left-{\frac{2\cos{2\(x - 4\ln5) }{\sin^2{{\c}{2\c}{\c}{\c}{\c}{\c}{\c}{\c}{\<|eot_id|>