x/frac{3{9}}+x/25/100+frac{x/2}{10}+frac{frac{x}{15}}{90} eching

$$\frac{ x }{ \frac{ 3 }{ 9 } } + \frac{ \frac{ x }{ 25 } }{ 100 } + \frac{ \frac{ x }{ 2 } }{ 10 } + \frac{ \frac{ x }{ 15 } }{ 90 }$$

Baholash

$$\frac{51488x}{16875}$$

Yechim qadamlari

x ni \frac{3}{9} ga bo'lish x ga k'paytirish \frac{3}{9} ga qaytarish.

$$\frac{x\times 9}{3}+\frac{\frac{x}{25}}{100}+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90}$$

x\times 3 ni olish uchun x\times 9 ni 3 ga bo‘ling.

$$x\times 3+\frac{\frac{x}{25}}{100}+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90}$$

\frac{\frac{x}{25}}{100} ni yagona kasrga aylantiring.

$$x\times 3+\frac{x}{25\times 100}+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90}$$

2500 hosil qilish uchun 25 va 100 ni ko'paytirish.

$$x\times 3+\frac{x}{2500}+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90}$$

\frac{7501}{2500}x ni olish uchun x\times 3 va \frac{x}{2500} ni birlashtirish.

$$\frac{7501}{2500}x+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90}$$

\frac{\frac{x}{2}}{10} ni yagona kasrga aylantiring.

$$\frac{7501}{2500}x+\frac{x}{2\times 10}+\frac{\frac{x}{15}}{90}$$

20 hosil qilish uchun 2 va 10 ni ko'paytirish.

$$\frac{7501}{2500}x+\frac{x}{20}+\frac{\frac{x}{15}}{90}$$

\frac{3813}{1250}x ni olish uchun \frac{7501}{2500}x va \frac{x}{20} ni birlashtirish.

$$\frac{3813}{1250}x+\frac{\frac{x}{15}}{90}$$

\frac{\frac{x}{15}}{90} ni yagona kasrga aylantiring.

$$\frac{3813}{1250}x+\frac{x}{15\times 90}$$

1350 hosil qilish uchun 15 va 90 ni ko'paytirish.

$$\frac{3813}{1250}x+\frac{x}{1350}$$

\frac{51488}{16875}x ni olish uchun \frac{3813}{1250}x va \frac{x}{1350} ni birlashtirish.

$$\frac{51488}{16875}x$$

x ga nisbatan hosilani topish

$$\frac{51488}{16875} = 3\frac{863}{16875} = 3,051140740740741$$

Derivativ ifodasidan foydalanish qadamlari

x ni \frac{3}{9} ga bo'lish x ga k'paytirish \frac{3}{9} ga qaytarish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x\times 9}{3}+\frac{\frac{x}{25}}{100}+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90})$$

x\times 3 ni olish uchun x\times 9 ni 3 ga bo‘ling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times 3+\frac{\frac{x}{25}}{100}+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90})$$

\frac{\frac{x}{25}}{100} ni yagona kasrga aylantiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times 3+\frac{x}{25\times 100}+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90})$$

2500 hosil qilish uchun 25 va 100 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times 3+\frac{x}{2500}+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90})$$

\frac{7501}{2500}x ni olish uchun x\times 3 va \frac{x}{2500} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7501}{2500}x+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90})$$

\frac{\frac{x}{2}}{10} ni yagona kasrga aylantiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7501}{2500}x+\frac{x}{2\times 10}+\frac{\frac{x}{15}}{90})$$

20 hosil qilish uchun 2 va 10 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7501}{2500}x+\frac{x}{20}+\frac{\frac{x}{15}}{90})$$

\frac{3813}{1250}x ni olish uchun \frac{7501}{2500}x va \frac{x}{20} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3813}{1250}x+\frac{\frac{x}{15}}{90})$$

\frac{\frac{x}{15}}{90} ni yagona kasrga aylantiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3813}{1250}x+\frac{x}{15\times 90})$$

1350 hosil qilish uchun 15 va 90 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3813}{1250}x+\frac{x}{1350})$$

\frac{51488}{16875}x ni olish uchun \frac{3813}{1250}x va \frac{x}{1350} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{51488}{16875}x)$$

ax^{n} hosilasi – nax^{n-1}.

$$\frac{51488}{16875}x^{1-1}$$

1 dan 1 ni ayirish.

$$\frac{51488}{16875}x^{0}$$

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

$$\frac{51488}{16875}\times 1$$

Har qanday t sharti uchun t\times 1=t va 1t=t.

$$\frac{51488}{16875}$$