f(x)=x/x^2-15x+50 eching

$$f ( x ) = \frac { x } { x ^ { 2 } - 15 x + 50 }$$

x ga nisbatan hosilani topish

$$\frac{50-x^{2}}{\left(\left(x-10\right)\left(x-5\right)\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

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

$$\frac{\left(x^{2}-15x^{1}+50\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1})-x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-15x^{1}+50)}{\left(x^{2}-15x^{1}+50\right)^{2}}$$

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

$$\frac{\left(x^{2}-15x^{1}+50\right)x^{1-1}-x^{1}\left(2x^{2-1}-15x^{1-1}\right)}{\left(x^{2}-15x^{1}+50\right)^{2}}$$

Qisqartirish.

$$\frac{\left(x^{2}-15x^{1}+50\right)x^{0}-x^{1}\left(2x^{1}-15x^{0}\right)}{\left(x^{2}-15x^{1}+50\right)^{2}}$$

x^{2}-15x^{1}+50 ni x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}x^{0}-15x^{1}x^{0}+50x^{0}-x^{1}\left(2x^{1}-15x^{0}\right)}{\left(x^{2}-15x^{1}+50\right)^{2}}$$

x^{1} ni 2x^{1}-15x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}x^{0}-15x^{1}x^{0}+50x^{0}-\left(x^{1}\times 2x^{1}+x^{1}\left(-15\right)x^{0}\right)}{\left(x^{2}-15x^{1}+50\right)^{2}}$$

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

$$\frac{x^{2}-15x^{1}+50x^{0}-\left(2x^{1+1}-15x^{1}\right)}{\left(x^{2}-15x^{1}+50\right)^{2}}$$

Qisqartirish.

$$\frac{x^{2}-15x^{1}+50x^{0}-\left(2x^{2}-15x^{1}\right)}{\left(x^{2}-15x^{1}+50\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{-x^{2}+50x^{0}}{\left(x^{2}-15x^{1}+50\right)^{2}}$$

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

$$\frac{-x^{2}+50x^{0}}{\left(x^{2}-15x+50\right)^{2}}$$

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

$$\frac{-x^{2}+50\times 1}{\left(x^{2}-15x+50\right)^{2}}$$

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

$$\frac{-x^{2}+50}{\left(x^{2}-15x+50\right)^{2}}$$

Baholash

$$\frac{x}{\left(x-10\right)\left(x-5\right)}$$