(3125t^125)^frac{1{3}} eching

$$( 3125 t ^ { 125 } ) ^ { \frac { 1 } { 3 } }$$

Baholash

$$5^{\frac{5}{3}}t^{\frac{125}{3}}$$

Oshib boruvchi tartibdan boshqa tartib uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\sqrt[3]{3125t^{125}}$$

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

$$\sqrt[3]{3125}\sqrt[3]{t^{125}}$$

3125 ni \frac{1}{3} daraja ko'rsatgichiga oshirish.

$$5\times 5^{\frac{2}{3}}\sqrt[3]{t^{125}}$$

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

$$5\times 5^{\frac{2}{3}}t^{125\times \frac{1}{3}}$$

125 ni \frac{1}{3} marotabaga ko'paytirish.

$$5\times 5^{\frac{2}{3}}t^{\frac{125}{3}}$$

t ga nisbatan hosilani topish

$$\frac{625\times 5^{\frac{2}{3}}t^{\frac{122}{3}}}{3}$$

Zanjirli qoidadan foydalanish qadamalari

Agar F ikki differensial funksiya f\left(u\right) va u=g\left(x\right)'ning yig'indisi bo'lsa, ya'ni agar F\left(x\right)=f\left(g\left(x\right)\right) bo'lsa, F hosilasi f'ning u martalik hosilasi, g'ning x martalik hosilasi ya'ni \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right) bo'ladi.

$$\frac{1}{3}\times \left(3125t^{125}\right)^{\frac{1}{3}-1}\frac{\mathrm{d}}{\mathrm{d}t}(3125t^{125})$$

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

$$\frac{1}{3}\times \left(3125t^{125}\right)^{-\frac{2}{3}}\times 125\times 3125t^{125-1}$$

Qisqartirish.

$$\frac{390625}{3}t^{124}\times \left(3125t^{125}\right)^{-\frac{2}{3}}$$