((1-x^2)^-frac{1{2}})^prime= eching

$$( ( 1 - x ^ { 2 } ) ^ { - \frac { 1 } { 2 } } ) ^ { \prime } =$$

Baholash

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

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.

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

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

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

Qisqartirish.

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

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

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

x ga nisbatan hosilani topish

$$\frac{2x^{2}+1}{\left(1-x^{2}\right)^{\frac{5}{2}}}$$