(36x^-4)^-frac{1{2}} eching

$$( 36 x ^ { - 4 } ) ^ { - \frac { 1 } { 2 } }$$

Baholash

$$\frac{x^{2}}{6}$$

Yechim qadamlari

\left(36x^{-4}\right)^{-\frac{1}{2}} ni kengaytirish.

$$36^{-\frac{1}{2}}\left(x^{-4}\right)^{-\frac{1}{2}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. -4 va -\frac{1}{2} ni ko‘paytirib, 2 ni oling.

$$36^{-\frac{1}{2}}x^{2}$$

-\frac{1}{2} daraja ko‘rsatkichini 36 ga hisoblang va \frac{1}{6} ni qiymatni oling.

$$\frac{1}{6}x^{2}$$

x ga nisbatan hosilani topish

$$\frac{x}{3}$$

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.

$$-\frac{1}{2}\times \left(36x^{-4}\right)^{-\frac{1}{2}-1}\frac{\mathrm{d}}{\mathrm{d}x}(36x^{-4})$$

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

$$-\frac{1}{2}\times \left(36x^{-4}\right)^{-\frac{3}{2}}\left(-4\right)\times 36x^{-4-1}$$

Qisqartirish.

$$72x^{-5}\times \left(36x^{-4}\right)^{-\frac{3}{2}}$$