d((1/15x)^10-(15x)^2+1)/dx eching

$$\frac { d ( ( \frac { 1 } { 15 } x ) ^ { 10 } - ( 15 x ) ^ { 2 } + 1 ) } { d x }$$

Baholash

$$\frac{2x^{9}}{115330078125}-450x$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

\left(\frac{1}{15}x\right)^{10} ni kengaytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(\frac{1}{15}\right)^{10}x^{10}-\left(15x\right)^{2}+1)$$

10 daraja ko‘rsatkichini \frac{1}{15} ga hisoblang va \frac{1}{576650390625} ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{576650390625}x^{10}-\left(15x\right)^{2}+1)$$

\left(15x\right)^{2} ni kengaytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{576650390625}x^{10}-15^{2}x^{2}+1)$$

2 daraja ko‘rsatkichini 15 ga hisoblang va 225 ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{576650390625}x^{10}-225x^{2}+1)$$

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

$$10\times \frac{1}{576650390625}x^{10-1}+2\left(-225\right)x^{2-1}$$

10 ni \frac{1}{576650390625} marotabaga ko'paytirish.

$$\frac{2}{115330078125}x^{10-1}+2\left(-225\right)x^{2-1}$$

10 dan 1 ni ayirish.

$$\frac{2}{115330078125}x^{9}+2\left(-225\right)x^{2-1}$$

2 ni -225 marotabaga ko'paytirish.

$$\frac{2}{115330078125}x^{9}-450x^{2-1}$$

2 dan 1 ni ayirish.

$$\frac{2}{115330078125}x^{9}-450x^{1}$$

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

$$\frac{2}{115330078125}x^{9}-450x$$

x ga nisbatan hosilani topish

$$\frac{2x^{8}}{12814453125}-450$$