d/dx(2x^3-3x)^-4 eching

$$\frac { d } { d x } ( 2 x ^ { 3 } - 3 x ) ^ { - 4 }$$

Baholash

$$\frac{12\left(1-2x^{2}\right)}{\left(x\left(2x^{2}-3\right)\right)^{5}}$$

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.

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

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

$$-4\left(2x^{3}-3x^{1}\right)^{-5}\left(3\times 2x^{3-1}-3x^{1-1}\right)$$

Qisqartirish.

$$\left(2x^{3}-3x^{1}\right)^{-5}\left(-24x^{2}+12x^{0}\right)$$

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

$$\left(2x^{3}-3x\right)^{-5}\left(-24x^{2}+12x^{0}\right)$$

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

$$\left(2x^{3}-3x\right)^{-5}\left(-24x^{2}+12\times 1\right)$$

Har qanday t sharti uchun t\times 1=t va 1t=t.

$$\left(2x^{3}-3x\right)^{-5}\left(-24x^{2}+12\right)$$

x ga nisbatan hosilani topish

$$\frac{12\left(52x^{4}-48x^{2}+15\right)}{\left(x\left(2x^{2}-3\right)\right)^{6}}$$