(16-x^2)+(-19x^2+7x^5-10x^4+5) eching

$$( 16 - x ^ { 2 } ) + ( - 19 x ^ { 2 } + 7 x ^ { 5 } - 10 x ^ { 4 } + 5 )$$

Baholash

$$7x^{5}-10x^{4}-20x^{2}+21$$

Yechim qadamlari

-20x^{2} ni olish uchun -x^{2} va -19x^{2} ni birlashtirish.

$$16-20x^{2}+7x^{5}-10x^{4}+5$$

21 olish uchun 16 va 5'ni qo'shing.

$$21-20x^{2}+7x^{5}-10x^{4}$$

x ga nisbatan hosilani topish

$$35x^{4}-40x^{3}-40x$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

-20x^{2} ni olish uchun -x^{2} va -19x^{2} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(16-20x^{2}+7x^{5}-10x^{4}+5)$$

21 olish uchun 16 va 5'ni qo'shing.

$$\frac{\mathrm{d}}{\mathrm{d}x}(21-20x^{2}+7x^{5}-10x^{4})$$

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

$$2\left(-20\right)x^{2-1}+5\times 7x^{5-1}+4\left(-10\right)x^{4-1}$$

2 ni -20 marotabaga ko'paytirish.

$$-40x^{2-1}+5\times 7x^{5-1}+4\left(-10\right)x^{4-1}$$

2 dan 1 ni ayirish.

$$-40x^{1}+5\times 7x^{5-1}+4\left(-10\right)x^{4-1}$$

5 ni 7 marotabaga ko'paytirish.

$$-40x^{1}+35x^{5-1}+4\left(-10\right)x^{4-1}$$

5 dan 1 ni ayirish.

$$-40x^{1}+35x^{4}+4\left(-10\right)x^{4-1}$$

5 ni 7 marotabaga ko'paytirish.

$$-40x^{1}+35x^{4}-40x^{4-1}$$

4 dan 1 ni ayirish.

$$-40x^{1}+35x^{4}-40x^{3}$$

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

$$-40x+35x^{4}-40x^{3}$$