Issolvi (1/2-1/4-1/6)x^12-25frac{5{6}}div(-5)

$$( \frac { 1 } { 2 } - \frac { 1 } { 4 } - \frac { 1 } { 6 } ) x ^ { 12 - 25 \frac { 5 } { 6 } } \div ( - 5 )$$

Evalwa

$$-\frac{1}{60x^{\frac{83}{6}}}$$

Passi tas-Soluzzjonijiet

Naqqas \frac{1}{4} minn \frac{1}{2} biex tikseb \frac{1}{4}.

$$\frac{\left(\frac{1}{4}-\frac{1}{6}\right)x^{12-\frac{25\times 6+5}{6}}}{-5}$$

Naqqas \frac{1}{6} minn \frac{1}{4} biex tikseb \frac{1}{12}.

$$\frac{\frac{1}{12}x^{12-\frac{25\times 6+5}{6}}}{-5}$$

Immultiplika 25 u 6 biex tikseb 150.

$$\frac{\frac{1}{12}x^{12-\frac{150+5}{6}}}{-5}$$

Żid 150 u 5 biex tikseb 155.

$$\frac{\frac{1}{12}x^{12-\frac{155}{6}}}{-5}$$

Naqqas \frac{155}{6} minn 12 biex tikseb -\frac{83}{6}.

$$\frac{\frac{1}{12}x^{-\frac{83}{6}}}{-5}$$

Iddividi \frac{1}{12}x^{-\frac{83}{6}} b'-5 biex tikseb-\frac{1}{60}x^{-\frac{83}{6}}.

$$-\frac{1}{60}x^{-\frac{83}{6}}$$

Iddifferenzja w.r.t. x

$$\frac{83}{360x^{\frac{89}{6}}}$$

Passi għall-Użu ta' Definizzjoni ta' Dervattiv

Naqqas \frac{1}{4} minn \frac{1}{2} biex tikseb \frac{1}{4}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(\frac{1}{4}-\frac{1}{6}\right)x^{12-\frac{25\times 6+5}{6}}}{-5})$$

Naqqas \frac{1}{6} minn \frac{1}{4} biex tikseb \frac{1}{12}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{1}{12}x^{12-\frac{25\times 6+5}{6}}}{-5})$$

Immultiplika 25 u 6 biex tikseb 150.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{1}{12}x^{12-\frac{150+5}{6}}}{-5})$$

Żid 150 u 5 biex tikseb 155.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{1}{12}x^{12-\frac{155}{6}}}{-5})$$

Naqqas \frac{155}{6} minn 12 biex tikseb -\frac{83}{6}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{1}{12}x^{-\frac{83}{6}}}{-5})$$

Iddividi \frac{1}{12}x^{-\frac{83}{6}} b'-5 biex tikseb-\frac{1}{60}x^{-\frac{83}{6}}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{1}{60}x^{-\frac{83}{6}})$$

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

$$-\frac{83}{6}\left(-\frac{1}{60}\right)x^{-\frac{83}{6}-1}$$

Immultiplika -\frac{83}{6} b'-\frac{1}{60} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur. Imbagħad naqqas il-frazzjoni għall-inqas termini jekk possibbli.

$$\frac{83}{360}x^{-\frac{83}{6}-1}$$

Naqqas 1 minn -\frac{83}{6}.

$$\frac{83}{360}x^{-\frac{89}{6}}$$