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5x^{2}-\frac{1}{2}x^{2}
5x^{2} ni olish uchun 2x^{2} va 3x^{2} ni birlashtirish.
\frac{9}{2}x^{2}
\frac{9}{2}x^{2} ni olish uchun 5x^{2} va -\frac{1}{2}x^{2} ni birlashtirish.
\frac{\mathrm{d}}{\mathrm{d}x}(5x^{2}-\frac{1}{2}x^{2})
5x^{2} ni olish uchun 2x^{2} va 3x^{2} ni birlashtirish.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{9}{2}x^{2})
\frac{9}{2}x^{2} ni olish uchun 5x^{2} va -\frac{1}{2}x^{2} ni birlashtirish.
2\times \frac{9}{2}x^{2-1}
ax^{n} hosilasi – nax^{n-1}.
9x^{2-1}
2 ni \frac{9}{2} marotabaga ko'paytirish.
9x^{1}
2 dan 1 ni ayirish.
9x
Har qanday t sharti uchun t^{1}=t.