Baholash
\frac{2x+3}{2x+1}
x ga nisbatan hosilani topish
-\frac{4}{\left(2x+1\right)^{2}}
Grafik
Baham ko'rish
Klipbordga nusxa olish
\frac{3}{\left(-x+1\right)\left(2x+1\right)}+\frac{x}{x-1}
Faktor: 1+x-2x^{2}.
\frac{3\left(-1\right)}{\left(x-1\right)\left(2x+1\right)}+\frac{x\left(2x+1\right)}{\left(x-1\right)\left(2x+1\right)}
Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(-x+1\right)\left(2x+1\right) va x-1 ning eng kichik umumiy karralisi \left(x-1\right)\left(2x+1\right). \frac{3}{\left(-x+1\right)\left(2x+1\right)} ni \frac{-1}{-1} marotabaga ko'paytirish. \frac{x}{x-1} ni \frac{2x+1}{2x+1} marotabaga ko'paytirish.
\frac{3\left(-1\right)+x\left(2x+1\right)}{\left(x-1\right)\left(2x+1\right)}
\frac{3\left(-1\right)}{\left(x-1\right)\left(2x+1\right)} va \frac{x\left(2x+1\right)}{\left(x-1\right)\left(2x+1\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.
\frac{-3+2x^{2}+x}{\left(x-1\right)\left(2x+1\right)}
3\left(-1\right)+x\left(2x+1\right) ichidagi ko‘paytirishlarni bajaring.
\frac{\left(x-1\right)\left(2x+3\right)}{\left(x-1\right)\left(2x+1\right)}
\frac{-3+2x^{2}+x}{\left(x-1\right)\left(2x+1\right)} ichida hali faktorlanmagan ifodalarni faktorlang.
\frac{2x+3}{2x+1}
Surat va maxrajdagi ikkala x-1 ni qisqartiring.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{\left(-x+1\right)\left(2x+1\right)}+\frac{x}{x-1})
Faktor: 1+x-2x^{2}.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\left(-1\right)}{\left(x-1\right)\left(2x+1\right)}+\frac{x\left(2x+1\right)}{\left(x-1\right)\left(2x+1\right)})
Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(-x+1\right)\left(2x+1\right) va x-1 ning eng kichik umumiy karralisi \left(x-1\right)\left(2x+1\right). \frac{3}{\left(-x+1\right)\left(2x+1\right)} ni \frac{-1}{-1} marotabaga ko'paytirish. \frac{x}{x-1} ni \frac{2x+1}{2x+1} marotabaga ko'paytirish.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\left(-1\right)+x\left(2x+1\right)}{\left(x-1\right)\left(2x+1\right)})
\frac{3\left(-1\right)}{\left(x-1\right)\left(2x+1\right)} va \frac{x\left(2x+1\right)}{\left(x-1\right)\left(2x+1\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-3+2x^{2}+x}{\left(x-1\right)\left(2x+1\right)})
3\left(-1\right)+x\left(2x+1\right) ichidagi ko‘paytirishlarni bajaring.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(x-1\right)\left(2x+3\right)}{\left(x-1\right)\left(2x+1\right)})
\frac{-3+2x^{2}+x}{\left(x-1\right)\left(2x+1\right)} ichida hali faktorlanmagan ifodalarni faktorlang.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x+3}{2x+1})
Surat va maxrajdagi ikkala x-1 ni qisqartiring.
\frac{\left(2x^{1}+1\right)\frac{\mathrm{d}}{\mathrm{d}x}(2x^{1}+3)-\left(2x^{1}+3\right)\frac{\mathrm{d}}{\mathrm{d}x}(2x^{1}+1)}{\left(2x^{1}+1\right)^{2}}
Har qanday ikki differensial funksiya uchun ikki funksiyaning koeffitsient hosilasi raqamlagichning hosila marotabasi maxraj minusi va barchasi kvadrat maxrajiga bo'lingan.
\frac{\left(2x^{1}+1\right)\times 2x^{1-1}-\left(2x^{1}+3\right)\times 2x^{1-1}}{\left(2x^{1}+1\right)^{2}}
Polinomialning hosilasi bu uning shartlari hosilasining yig‘indisiga teng. Konstant shartning hosilasi 0. ax^{n} ning hosilasi nax^{n-1}.
\frac{\left(2x^{1}+1\right)\times 2x^{0}-\left(2x^{1}+3\right)\times 2x^{0}}{\left(2x^{1}+1\right)^{2}}
Arifmetik hisobni amalga oshirish.
\frac{2x^{1}\times 2x^{0}+2x^{0}-\left(2x^{1}\times 2x^{0}+3\times 2x^{0}\right)}{\left(2x^{1}+1\right)^{2}}
Distributiv xususiyatdan foydalanib kengaytirish.
\frac{2\times 2x^{1}+2x^{0}-\left(2\times 2x^{1}+3\times 2x^{0}\right)}{\left(2x^{1}+1\right)^{2}}
Ayni daraja ko'rsatkichlarini ko'paytirish uchun ularning darajalarini qo'shing.
\frac{4x^{1}+2x^{0}-\left(4x^{1}+6x^{0}\right)}{\left(2x^{1}+1\right)^{2}}
Arifmetik hisobni amalga oshirish.
\frac{4x^{1}+2x^{0}-4x^{1}-6x^{0}}{\left(2x^{1}+1\right)^{2}}
Keraksiz qavslarni olib tashlash.
\frac{\left(4-4\right)x^{1}+\left(2-6\right)x^{0}}{\left(2x^{1}+1\right)^{2}}
O'xshash hadlarni birlashtirish.
\frac{-4x^{0}}{\left(2x^{1}+1\right)^{2}}
4 dan 4 ni va 2 dan 6 ni ayiring.
\frac{-4x^{0}}{\left(2x+1\right)^{2}}
Har qanday t sharti uchun t^{1}=t.
\frac{-4}{\left(2x+1\right)^{2}}
Har qanday t sharti uchun (0 bundan mustasno) t^{0}=1.
Misollar
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Matritsa
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Simli tenglama
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Differensatsiya
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Oʻngga
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Chegaralar
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