1/(x^2-25)+6/(5+x) eching

$$1 / ( x ^ { 2 } - 25 ) + 6 / ( 5 + x )$$

Baholash

$$\frac{6x-29}{x^{2}-25}$$

Qisqa yechim qadamlari

Faktor: x^{2}-25.

$$\frac{1}{\left(x-5\right)\left(x+5\right)}+\frac{6}{5+x}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(x-5\right)\left(x+5\right) va 5+x ning eng kichik umumiy karralisi \left(x-5\right)\left(x+5\right). \frac{6}{5+x} ni \frac{x-5}{x-5} marotabaga ko'paytirish.

$$\frac{1}{\left(x-5\right)\left(x+5\right)}+\frac{6\left(x-5\right)}{\left(x-5\right)\left(x+5\right)}$$

\frac{1}{\left(x-5\right)\left(x+5\right)} va \frac{6\left(x-5\right)}{\left(x-5\right)\left(x+5\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{1+6\left(x-5\right)}{\left(x-5\right)\left(x+5\right)}$$

1+6\left(x-5\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{1+6x-30}{\left(x-5\right)\left(x+5\right)}$$

1+6x-30 kabi iboralarga o‘xshab birlashtiring.

$$\frac{-29+6x}{\left(x-5\right)\left(x+5\right)}$$

\left(x-5\right)\left(x+5\right) ni kengaytirish.

$$\frac{-29+6x}{x^{2}-25}$$

x ga nisbatan hosilani topish

$$\frac{2\left(-3x^{2}+29x-75\right)}{\left(x^{2}-25\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Faktor: x^{2}-25.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{\left(x-5\right)\left(x+5\right)}+\frac{6}{5+x})$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(x-5\right)\left(x+5\right) va 5+x ning eng kichik umumiy karralisi \left(x-5\right)\left(x+5\right). \frac{6}{5+x} ni \frac{x-5}{x-5} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{\left(x-5\right)\left(x+5\right)}+\frac{6\left(x-5\right)}{\left(x-5\right)\left(x+5\right)})$$

\frac{1}{\left(x-5\right)\left(x+5\right)} va \frac{6\left(x-5\right)}{\left(x-5\right)\left(x+5\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1+6\left(x-5\right)}{\left(x-5\right)\left(x+5\right)})$$

1+6\left(x-5\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1+6x-30}{\left(x-5\right)\left(x+5\right)})$$

1+6x-30 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-29+6x}{\left(x-5\right)\left(x+5\right)})$$

Hisoblang: \left(x-5\right)\left(x+5\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 5 kvadratini chiqarish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-29+6x}{x^{2}-25})$$

Har qanday ikki differensial funksiya uchun ikki funksiyaning koeffitsient hosilasi raqamlagichning hosila marotabasi maxraj minusi va barchasi kvadrat maxrajiga bo'lingan.

$$\frac{\left(x^{2}-25\right)\frac{\mathrm{d}}{\mathrm{d}x}(6x^{1}-29)-\left(6x^{1}-29\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-25)}{\left(x^{2}-25\right)^{2}}$$

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

$$\frac{\left(x^{2}-25\right)\times 6x^{1-1}-\left(6x^{1}-29\right)\times 2x^{2-1}}{\left(x^{2}-25\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(x^{2}-25\right)\times 6x^{0}-\left(6x^{1}-29\right)\times 2x^{1}}{\left(x^{2}-25\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{x^{2}\times 6x^{0}-25\times 6x^{0}-\left(6x^{1}\times 2x^{1}-29\times 2x^{1}\right)}{\left(x^{2}-25\right)^{2}}$$

Ayni daraja ko'rsatkichlarini ko'paytirish uchun ularning darajalarini qo'shing.

$$\frac{6x^{2}-25\times 6x^{0}-\left(6\times 2x^{1+1}-29\times 2x^{1}\right)}{\left(x^{2}-25\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{6x^{2}-150x^{0}-\left(12x^{2}-58x^{1}\right)}{\left(x^{2}-25\right)^{2}}$$

Keraksiz qavslarni olib tashlash.

$$\frac{6x^{2}-150x^{0}-12x^{2}-\left(-58x^{1}\right)}{\left(x^{2}-25\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(6-12\right)x^{2}-150x^{0}-\left(-58x^{1}\right)}{\left(x^{2}-25\right)^{2}}$$

6 dan 12 ni ayirish.

$$\frac{-6x^{2}-150x^{0}-\left(-58x^{1}\right)}{\left(x^{2}-25\right)^{2}}$$

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

$$\frac{-6x^{2}-150x^{0}-\left(-58x\right)}{\left(x^{2}-25\right)^{2}}$$

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

$$\frac{-6x^{2}-150-\left(-58x\right)}{\left(x^{2}-25\right)^{2}}$$