d/dxleft(cot(3x)right) eching

$$\frac{d}{d x } \left( \cot ( 3x ) \right)$$

Baholash

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

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.

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

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

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

Qisqartirish.

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

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

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

x ga nisbatan hosilani topish

$$\frac{18\cot(x)\left(3\left(\sin(x)\right)^{2}-\left(\cos(x)\right)^{2}\right)}{\left(\sin(x)\right)^{2}\left(\left(\sin(x)\right)^{2}-3\left(\cos(x)\right)^{2}\right)\left(3\left(\cos(x)\right)^{2}-\left(\sin(x)\right)^{2}\right)^{2}}$$