Issolvi 4sqrt{15/8}u1/5sqrt{750}

$$4 \sqrt { \frac { 15 } { 8 } } u \frac { 1 } { 5 } \sqrt { 750 }$$

Evalwa

$$30u$$

Passi tas-Soluzzjonijiet

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{15}{8}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{15}}{\sqrt{8}}.

$$4\times \frac{\sqrt{15}}{\sqrt{8}}u\times \frac{1}{5}\sqrt{750}$$

Iffattura 8=2^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 2^{2}.

$$4\times \frac{\sqrt{15}}{2\sqrt{2}}u\times \frac{1}{5}\sqrt{750}$$

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{15}}{2\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}.

$$4\times \frac{\sqrt{15}\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}u\times \frac{1}{5}\sqrt{750}$$

Il-kwadrat ta' \sqrt{2} huwa 2.

$$4\times \frac{\sqrt{15}\sqrt{2}}{2\times 2}u\times \frac{1}{5}\sqrt{750}$$

Biex timmultiplika \sqrt{15} u \sqrt{2}, immultiplika n-numri taħt l-għerq kwadrat.

$$4\times \frac{\sqrt{30}}{2\times 2}u\times \frac{1}{5}\sqrt{750}$$

Immultiplika 2 u 2 biex tikseb 4.

$$4\times \frac{\sqrt{30}}{4}u\times \frac{1}{5}\sqrt{750}$$

Immultiplika 4 u \frac{1}{5} biex tikseb \frac{4}{5}.

$$\frac{4}{5}\times \frac{\sqrt{30}}{4}u\sqrt{750}$$

Iffattura 750=5^{2}\times 30. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{5^{2}\times 30} bħala l-prodott tal-għeruq kwadrati \sqrt{5^{2}}\sqrt{30}. Ħu l-għerq kwadrat ta' 5^{2}.

$$\frac{4}{5}\times \frac{\sqrt{30}}{4}u\times 5\sqrt{30}$$

Annulla 5 u 5.

$$4\times \frac{\sqrt{30}}{4}u\sqrt{30}$$

Annulla 4 u 4.

$$\sqrt{30}u\sqrt{30}$$

Immultiplika \sqrt{30} u \sqrt{30} biex tikseb 30.

$$30u$$

Iddifferenzja w.r.t. u

$$30$$

Passi għall-Użu ta' Definizzjoni ta' Dervattiv

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{15}{8}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{15}}{\sqrt{8}}.

$$\frac{\mathrm{d}}{\mathrm{d}u}(4\times \frac{\sqrt{15}}{\sqrt{8}}u\times \frac{1}{5}\sqrt{750})$$

Iffattura 8=2^{2}\times 2. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{2^{2}\times 2} bħala l-prodott tal-għeruq kwadrati \sqrt{2^{2}}\sqrt{2}. Ħu l-għerq kwadrat ta' 2^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}u}(4\times \frac{\sqrt{15}}{2\sqrt{2}}u\times \frac{1}{5}\sqrt{750})$$

Irrazzjonalizza d-denominatur tal-\frac{\sqrt{15}}{2\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{2}.

$$\frac{\mathrm{d}}{\mathrm{d}u}(4\times \frac{\sqrt{15}\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}u\times \frac{1}{5}\sqrt{750})$$

Il-kwadrat ta' \sqrt{2} huwa 2.

$$\frac{\mathrm{d}}{\mathrm{d}u}(4\times \frac{\sqrt{15}\sqrt{2}}{2\times 2}u\times \frac{1}{5}\sqrt{750})$$

Biex timmultiplika \sqrt{15} u \sqrt{2}, immultiplika n-numri taħt l-għerq kwadrat.

$$\frac{\mathrm{d}}{\mathrm{d}u}(4\times \frac{\sqrt{30}}{2\times 2}u\times \frac{1}{5}\sqrt{750})$$

Immultiplika 2 u 2 biex tikseb 4.

$$\frac{\mathrm{d}}{\mathrm{d}u}(4\times \frac{\sqrt{30}}{4}u\times \frac{1}{5}\sqrt{750})$$

Immultiplika 4 u \frac{1}{5} biex tikseb \frac{4}{5}.

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{4}{5}\times \frac{\sqrt{30}}{4}u\sqrt{750})$$

Iffattura 750=5^{2}\times 30. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{5^{2}\times 30} bħala l-prodott tal-għeruq kwadrati \sqrt{5^{2}}\sqrt{30}. Ħu l-għerq kwadrat ta' 5^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{4}{5}\times \frac{\sqrt{30}}{4}u\times 5\sqrt{30})$$

Annulla 5 u 5.

$$\frac{\mathrm{d}}{\mathrm{d}u}(4\times \frac{\sqrt{30}}{4}u\sqrt{30})$$

Annulla 4 u 4.

$$\frac{\mathrm{d}}{\mathrm{d}u}(\sqrt{30}u\sqrt{30})$$

Immultiplika \sqrt{30} u \sqrt{30} biex tikseb 30.

$$\frac{\mathrm{d}}{\mathrm{d}u}(30u)$$

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

$$30u^{1-1}$$

Naqqas 1 minn 1.

$$30u^{0}$$

Għal kwalunkwe terminu t ħlief 0, t^{0}=1.

$$30\times 1$$

Għal kwalunkwe terminu t, t\times 1=t u 1t=t.

$$30$$