x^7/2*x^5/2= eching

$$x ^ { 7 / 2 } \cdot x ^ { 5 / 2 } =$$

x ga nisbatan hosilani topish

$$6x^{5}$$

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.

$$x^{\frac{7}{2}}\frac{\mathrm{d}}{\mathrm{d}x}(x^{\frac{5}{2}})+x^{\frac{5}{2}}\frac{\mathrm{d}}{\mathrm{d}x}(x^{\frac{7}{2}})$$

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

$$x^{\frac{7}{2}}\times \frac{5}{2}x^{\frac{5}{2}-1}+x^{\frac{5}{2}}\times \frac{7}{2}x^{\frac{7}{2}-1}$$

Qisqartirish.

$$x^{\frac{7}{2}}\times \frac{5}{2}x^{\frac{3}{2}}+x^{\frac{5}{2}}\times \frac{7}{2}x^{\frac{5}{2}}$$

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

$$\frac{5}{2}x^{\frac{7+3}{2}}+\frac{7}{2}x^{\frac{5+5}{2}}$$

Qisqartirish.

$$\frac{5}{2}x^{5}+\frac{7}{2}x^{5}$$

O'xshash hadlarni birlashtirish.

$$\frac{5+7}{2}x^{5}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{5}{2} ni \frac{7}{2} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$6x^{5}$$

Baholash

$$x^{6}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. \frac{7}{2} va \frac{5}{2} ni qo‘shib, 6 ni oling.

$$x^{6}$$