d/dxleft(1/frac{1{x}+1/7+1/8}right) eching

$$\frac{d}{d x } \left( \frac{ 1 }{ \frac{ 1 }{ x } + \frac{ 1 }{ 7 } + \frac{ 1 }{ 8 } } \right)$$

Baholash

$$\frac{3136}{\left(15x+56\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

7 va 8 ning eng kichik umumiy karralisi 56 ga teng. \frac{1}{7} va \frac{1}{8} ni 56 maxraj bilan kasrlarga aylantirib oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{\frac{1}{x}+\frac{8}{56}+\frac{7}{56}})$$

\frac{8}{56} va \frac{7}{56} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{\frac{1}{x}+\frac{8+7}{56}})$$

15 olish uchun 8 va 7'ni qo'shing.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{\frac{1}{x}+\frac{15}{56}})$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x va 56 ning eng kichik umumiy karralisi 56x. \frac{1}{x} ni \frac{56}{56} marotabaga ko'paytirish. \frac{15}{56} ni \frac{x}{x} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{\frac{56}{56x}+\frac{15x}{56x}})$$

\frac{56}{56x} va \frac{15x}{56x} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{\frac{56+15x}{56x}})$$

1 ni \frac{56+15x}{56x} ga bo'lish 1 ga k'paytirish \frac{56+15x}{56x} ga qaytarish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{56x}{56+15x})$$

Har qanday ikki differensial funksiya uchun ikki funksiyaning koeffitsient hosilasi raqamlagichning hosila marotabasi maxraj minusi va barchasi kvadrat maxrajiga bo'lingan.

$$\frac{\left(15x^{1}+56\right)\frac{\mathrm{d}}{\mathrm{d}x}(56x^{1})-56x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(15x^{1}+56)}{\left(15x^{1}+56\right)^{2}}$$

Polinomialning hosilasi bu uning shartlari hosilasining yig‘indisiga teng. Konstant shartning hosilasi 0. ax^{n} ning hosilasi nax^{n-1}.

$$\frac{\left(15x^{1}+56\right)\times 56x^{1-1}-56x^{1}\times 15x^{1-1}}{\left(15x^{1}+56\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(15x^{1}+56\right)\times 56x^{0}-56x^{1}\times 15x^{0}}{\left(15x^{1}+56\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{15x^{1}\times 56x^{0}+56\times 56x^{0}-56x^{1}\times 15x^{0}}{\left(15x^{1}+56\right)^{2}}$$

Ayni daraja ko'rsatkichlarini ko'paytirish uchun ularning darajalarini qo'shing.

$$\frac{15\times 56x^{1}+56\times 56x^{0}-56\times 15x^{1}}{\left(15x^{1}+56\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{840x^{1}+3136x^{0}-840x^{1}}{\left(15x^{1}+56\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(840-840\right)x^{1}+3136x^{0}}{\left(15x^{1}+56\right)^{2}}$$

840 dan 840 ni ayirish.

$$\frac{3136x^{0}}{\left(15x^{1}+56\right)^{2}}$$

Har qanday t sharti uchun t^{1}=t.

$$\frac{3136x^{0}}{\left(15x+56\right)^{2}}$$

Har qanday t sharti uchun (0 bundan mustasno) t^{0}=1.

$$\frac{3136\times 1}{\left(15x+56\right)^{2}}$$

Har qanday t sharti uchun t\times 1=t va 1t=t.

$$\frac{3136}{\left(15x+56\right)^{2}}$$

x ga nisbatan hosilani topish

$$-\frac{94080}{\left(15x+56\right)^{3}}$$