d/dx(1/sqrt{x+3})^2 eching

$$\frac { d } { d x } ( \frac { 1 } { \sqrt { x + 3 } } ) ^ { 2 }$$

Baholash

$$-\frac{1}{\left(x+3\right)^{2}}$$

Zanjirli qoidadan foydalanish qadamalari

\frac{1}{\sqrt{x+3}}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1^{2}}{\left(\sqrt{x+3}\right)^{2}})$$

2 daraja ko‘rsatkichini 1 ga hisoblang va 1 ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{\left(\sqrt{x+3}\right)^{2}})$$

2 daraja ko‘rsatkichini \sqrt{x+3} ga hisoblang va x+3 ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{x+3})$$

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.

$$-\left(x^{1}+3\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}+3)$$

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

$$-\left(x^{1}+3\right)^{-2}x^{1-1}$$

Qisqartirish.

$$-x^{0}\left(x^{1}+3\right)^{-2}$$

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

$$-x^{0}\left(x+3\right)^{-2}$$

Har qanday t sharti uchun (0 bundan mustasno) t^{0}=1.

$$-\left(x+3\right)^{-2}$$

x ga nisbatan hosilani topish

$$\frac{2}{\left(x+3\right)^{3}}$$