14y/42y^2 eching

$$\frac { 14 y } { 42 y ^ { 2 } }$$

Baholash

$$\frac{1}{3y}$$

Ikki eksponentning koʻpaytmasi uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\left(14y^{1}\right)^{1}\times \frac{1}{42y^{2}}$$

Ikki yoki undan ko'p raqam koʻpaytmasini daraja ko'rsatkichiga oshirish uchun har bir raqamni daraja ko'rsatkichiga oshiring va ularning koʻpaytmasini chiqaring.

$$14^{1}\left(y^{1}\right)^{1}\times \frac{1}{42}\times \frac{1}{y^{2}}$$

Ko'paytirishning kommutativ xususiyatidan foydalanish.

$$14^{1}\times \frac{1}{42}\left(y^{1}\right)^{1}\times \frac{1}{y^{2}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring.

$$14^{1}\times \frac{1}{42}y^{1}y^{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$14^{1}\times \frac{1}{42}y^{1}y^{-2}$$

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

$$14^{1}\times \frac{1}{42}y^{1-2}$$

1 va -2 belgilarini qo'shish.

$$14^{1}\times \frac{1}{42}\times \frac{1}{y}$$

14 ni 1 daraja ko'rsatgichiga oshirish.

$$14\times \frac{1}{42}\times \frac{1}{y}$$

14 ni \frac{1}{42} marotabaga ko'paytirish.

$$\frac{1}{3}\times \frac{1}{y}$$

Eksponent koeffitsienti uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\frac{14^{1}y^{1}}{42^{1}y^{2}}$$

Ayni asosning daraja ko'rsatkichi bo'lish uchun maxrajning darajasini surat darajasidan bo'ling.

$$\frac{14^{1}y^{1-2}}{42^{1}}$$

1 dan 2 ni ayirish.

$$\frac{14^{1}\times \frac{1}{y}}{42^{1}}$$

\frac{14}{42} ulushini 14 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{3}\times \frac{1}{y}$$

y ga nisbatan hosilani topish

$$-\frac{1}{3y^{2}}$$

Yechim qadamlari

Ayni asosning daraja ko'rsatkichi bo'lish uchun maxrajning darajasini surat darajasidan bo'ling.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{14}{42}y^{1-2})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{3}\times \frac{1}{y})$$

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

$$-\frac{1}{3}y^{-1-1}$$

Arifmetik hisobni amalga oshirish.

$$-\frac{1}{3}y^{-2}$$