Whakaoti i te d/dxleft(1/frac{1{x}+1/7+1/8}right)

$$\frac{d}{d x } \left( \frac{ 1 }{ \frac{ 1 }{ x } + \frac{ 1 }{ 7 } + \frac{ 1 }{ 8 } } \right)$$

Aromātai

$$\frac{3136}{\left(15x+56\right)^{2}}$$

Ngā Upane e Whakamahi ana i te Ture Pārōnaki mō te Otinga

Ko te maha noa iti rawa atu o 7 me 8 ko 56. Me tahuri \frac{1}{7} me \frac{1}{8} ki te hautau me te tautūnga 56.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{\frac{1}{x}+\frac{8}{56}+\frac{7}{56}})$$

Tā te mea he rite te tauraro o \frac{8}{56} me \frac{7}{56}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{\frac{1}{x}+\frac{8+7}{56}})$$

Tāpirihia te 8 ki te 7, ka 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{\frac{1}{x}+\frac{15}{56}})$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o x me 56 ko 56x. Whakareatia \frac{1}{x} ki te \frac{56}{56}. Whakareatia \frac{15}{56} ki te \frac{x}{x}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{\frac{56}{56x}+\frac{15x}{56x}})$$

Tā te mea he rite te tauraro o \frac{56}{56x} me \frac{15x}{56x}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{\frac{56+15x}{56x}})$$

Whakawehe 1 ki te \frac{56+15x}{56x} mā te whakarea 1 ki te tau huripoki o \frac{56+15x}{56x}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{56x}{56+15x})$$

Mō ngā pānga e rua e taea ana te pārōnaki, ko te pārōnaki o te otinga o ngā pānga e rua ko te tauraro whakareatia ki te pārōnaki o te taurunga tango i te taurunga whakareatia ki te pārōnaki o te tauraro, ā, ka whakawehea te katoa ki te tauraro kua pūruatia.

$$\frac{\left(15x^{1}+56\right)\frac{\mathrm{d}}{\mathrm{d}x}(56x^{1})-56x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(15x^{1}+56)}{\left(15x^{1}+56\right)^{2}}$$

Ko te pārōnaki o tētahi pūrau ko te tapeke o ngā pārōnaki o ōna kīanga tau. Ko te pārōnaki o tētahi kīanga tau pūmau ko 0. Ko te pārōnaki o te ax^{n} ko te nax^{n-1}.

$$\frac{\left(15x^{1}+56\right)\times 56x^{1-1}-56x^{1}\times 15x^{1-1}}{\left(15x^{1}+56\right)^{2}}$$

Mahia ngā tātaitanga.

$$\frac{\left(15x^{1}+56\right)\times 56x^{0}-56x^{1}\times 15x^{0}}{\left(15x^{1}+56\right)^{2}}$$

Whakarohaina mā te āhuatanga tohatoha.

$$\frac{15x^{1}\times 56x^{0}+56\times 56x^{0}-56x^{1}\times 15x^{0}}{\left(15x^{1}+56\right)^{2}}$$

Hei whakarea pū o te pūtake ōrite, tāpiri ana taupū.

$$\frac{15\times 56x^{1}+56\times 56x^{0}-56\times 15x^{1}}{\left(15x^{1}+56\right)^{2}}$$

Mahia ngā tātaitanga.

$$\frac{840x^{1}+3136x^{0}-840x^{1}}{\left(15x^{1}+56\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{\left(840-840\right)x^{1}+3136x^{0}}{\left(15x^{1}+56\right)^{2}}$$

Tango 840 mai i 840.

$$\frac{3136x^{0}}{\left(15x^{1}+56\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{3136x^{0}}{\left(15x+56\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{3136\times 1}{\left(15x+56\right)^{2}}$$

Mō tētahi kupu t, t\times 1=t me 1t=t.

$$\frac{3136}{\left(15x+56\right)^{2}}$$

Kimi Pārōnaki e ai ki x

$$-\frac{94080}{\left(15x+56\right)^{3}}$$