Issolvi 10^-63^-7625*x^-4div5^-3*{6}^-5*{x}^-8

$${ 10 }^{ -6 } { 3 }^{ -7 } 625 \times { x }^{ -4 } \div { 5 }^{ -3 } \times { 6 }^{ -5 } \times { x }^{ -8 }$$

Evalwa

$$\frac{5}{1088391168x^{12}}$$

Passi tas-Soluzzjonijiet

Ikkalkula 10 bil-power ta' -6 u tikseb \frac{1}{1000000}.

$$\frac{\frac{1}{1000000}\times 3^{-7}\times 625x^{-4}}{5^{-3}}\times 6^{-5}x^{-8}$$

Ikkalkula 3 bil-power ta' -7 u tikseb \frac{1}{2187}.

$$\frac{\frac{1}{1000000}\times \frac{1}{2187}\times 625x^{-4}}{5^{-3}}\times 6^{-5}x^{-8}$$

Immultiplika \frac{1}{1000000} u \frac{1}{2187} biex tikseb \frac{1}{2187000000}.

$$\frac{\frac{1}{2187000000}\times 625x^{-4}}{5^{-3}}\times 6^{-5}x^{-8}$$

Immultiplika \frac{1}{2187000000} u 625 biex tikseb \frac{1}{3499200}.

$$\frac{\frac{1}{3499200}x^{-4}}{5^{-3}}\times 6^{-5}x^{-8}$$

Ikkalkula 5 bil-power ta' -3 u tikseb \frac{1}{125}.

$$\frac{\frac{1}{3499200}x^{-4}}{\frac{1}{125}}\times 6^{-5}x^{-8}$$

Iddividi \frac{1}{3499200}x^{-4} b'\frac{1}{125} billi timmultiplika \frac{1}{3499200}x^{-4} bir-reċiproku ta' \frac{1}{125}.

$$\frac{1}{3499200}x^{-4}\times 125\times 6^{-5}x^{-8}$$

Immultiplika \frac{1}{3499200} u 125 biex tikseb \frac{5}{139968}.

$$\frac{5}{139968}x^{-4}\times 6^{-5}x^{-8}$$

Ikkalkula 6 bil-power ta' -5 u tikseb \frac{1}{7776}.

$$\frac{5}{139968}x^{-4}\times \frac{1}{7776}x^{-8}$$

Immultiplika \frac{5}{139968} u \frac{1}{7776} biex tikseb \frac{5}{1088391168}.

$$\frac{5}{1088391168}x^{-4}x^{-8}$$

Biex timmultiplika l-qawwa tal-istess bażi, żid l-esponenti tagħhom. Żid -4 u -8 biex tikseb -12.

$$\frac{5}{1088391168}x^{-12}$$

Iddifferenzja w.r.t. x

$$-\frac{5}{90699264x^{13}}$$

Passi għall-Użu ta' Definizzjoni ta' Dervattiv

Ikkalkula 10 bil-power ta' -6 u tikseb \frac{1}{1000000}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{1}{1000000}\times 3^{-7}\times 625x^{-4}}{5^{-3}}\times 6^{-5}x^{-8})$$

Ikkalkula 3 bil-power ta' -7 u tikseb \frac{1}{2187}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{1}{1000000}\times \frac{1}{2187}\times 625x^{-4}}{5^{-3}}\times 6^{-5}x^{-8})$$

Immultiplika \frac{1}{1000000} u \frac{1}{2187} biex tikseb \frac{1}{2187000000}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{1}{2187000000}\times 625x^{-4}}{5^{-3}}\times 6^{-5}x^{-8})$$

Immultiplika \frac{1}{2187000000} u 625 biex tikseb \frac{1}{3499200}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{1}{3499200}x^{-4}}{5^{-3}}\times 6^{-5}x^{-8})$$

Ikkalkula 5 bil-power ta' -3 u tikseb \frac{1}{125}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{1}{3499200}x^{-4}}{\frac{1}{125}}\times 6^{-5}x^{-8})$$

Iddividi \frac{1}{3499200}x^{-4} b'\frac{1}{125} billi timmultiplika \frac{1}{3499200}x^{-4} bir-reċiproku ta' \frac{1}{125}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{3499200}x^{-4}\times 125\times 6^{-5}x^{-8})$$

Immultiplika \frac{1}{3499200} u 125 biex tikseb \frac{5}{139968}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{139968}x^{-4}\times 6^{-5}x^{-8})$$

Ikkalkula 6 bil-power ta' -5 u tikseb \frac{1}{7776}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{139968}x^{-4}\times \frac{1}{7776}x^{-8})$$

Immultiplika \frac{5}{139968} u \frac{1}{7776} biex tikseb \frac{5}{1088391168}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{1088391168}x^{-4}x^{-8})$$

Biex timmultiplika l-qawwa tal-istess bażi, żid l-esponenti tagħhom. Żid -4 u -8 biex tikseb -12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{1088391168}x^{-12})$$

Id-derivattiv ta' ax^{n} huwa nax^{n-1}.

$$-12\times \frac{5}{1088391168}x^{-12-1}$$

Immultiplika -12 b'\frac{5}{1088391168}.

$$-\frac{5}{90699264}x^{-12-1}$$

Naqqas 1 minn -12.

$$-\frac{5}{90699264}x^{-13}$$