a^frac{1{2}}*a^frac{3{2}} eching

$$a ^ { \frac { 1 } { 2 } } \times a ^ { \frac { 3 } { 2 } }$$

a ga nisbatan hosilani topish

$$2a$$

Koʻpaytma uchun derivativ qoidasidan foydalanish qadamlari

Har qanday ikki differensial funksiya uchun, ikki funksiya koʻpaytmasining hosilasi birinchi funksiya marotabasi, ikkinchi plyus hosilasi ikkinchi funksiya marotabasi birinchining hosilasidir.

$$\sqrt{a}\frac{\mathrm{d}}{\mathrm{d}a}(a^{\frac{3}{2}})+a^{\frac{3}{2}}\frac{\mathrm{d}}{\mathrm{d}a}(\sqrt{a})$$

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

$$\sqrt{a}\times \frac{3}{2}a^{\frac{3}{2}-1}+a^{\frac{3}{2}}\times \frac{1}{2}a^{\frac{1}{2}-1}$$

Qisqartirish.

$$\sqrt{a}\times \frac{3}{2}\sqrt{a}+a^{\frac{3}{2}}\times \frac{1}{2}a^{-\frac{1}{2}}$$

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

$$\frac{3}{2}a^{\frac{1+1}{2}}+\frac{1}{2}a^{\frac{3-1}{2}}$$

Qisqartirish.

$$\frac{3}{2}a^{1}+\frac{1}{2}a^{1}$$

O'xshash hadlarni birlashtirish.

$$\frac{3+1}{2}a^{1}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{3}{2} ni \frac{1}{2} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$2a^{1}$$

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

$$2a$$

Baholash

$$a^{2}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. \frac{1}{2} va \frac{3}{2} ni qo‘shib, 2 ni oling.

$$a^{2}$$