5x/x^2-5x eching

$$\frac { 5 x } { x ^ { 2 } - 5 x }$$

Baholash

$$\frac{5}{x-5}$$

Qisqa yechim qadamlari

Hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala x ni qisqartiring.

$$\frac{5}{x-5}$$

x ga nisbatan hosilani topish

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

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.

$$\frac{\left(x^{2}-5x^{1}\right)\frac{\mathrm{d}}{\mathrm{d}x}(5x^{1})-5x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-5x^{1})}{\left(x^{2}-5x^{1}\right)^{2}}$$

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

$$\frac{\left(x^{2}-5x^{1}\right)\times 5x^{1-1}-5x^{1}\left(2x^{2-1}-5x^{1-1}\right)}{\left(x^{2}-5x^{1}\right)^{2}}$$

Qisqartirish.

$$\frac{\left(x^{2}-5x^{1}\right)\times 5x^{0}-5x^{1}\left(2x^{1}-5x^{0}\right)}{\left(x^{2}-5x^{1}\right)^{2}}$$

x^{2}-5x^{1} ni 5x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}\times 5x^{0}-5x^{1}\times 5x^{0}-5x^{1}\left(2x^{1}-5x^{0}\right)}{\left(x^{2}-5x^{1}\right)^{2}}$$

5x^{1} ni 2x^{1}-5x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}\times 5x^{0}-5x^{1}\times 5x^{0}-\left(5x^{1}\times 2x^{1}+5x^{1}\left(-5\right)x^{0}\right)}{\left(x^{2}-5x^{1}\right)^{2}}$$

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

$$\frac{5x^{2}-5\times 5x^{1}-\left(5\times 2x^{1+1}+5\left(-5\right)x^{1}\right)}{\left(x^{2}-5x^{1}\right)^{2}}$$

Qisqartirish.

$$\frac{5x^{2}-25x^{1}-\left(10x^{2}-25x^{1}\right)}{\left(x^{2}-5x^{1}\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{-5x^{2}}{\left(x^{2}-5x^{1}\right)^{2}}$$

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

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