The wanda aka samu daga cikin ba tare da na kwana ne daidaita da cosine na wannan kwana

Dana sauki trigonometry aiki y = Zunubi (x), shi ne differentiable a kowane batu na dukan yankin. Dole ne mu tabbatar da cewa da wanda aka samu daga cikin ba tare da na wata hujja ne daidaita da cosine na wannan kusurwa, wato, '= cos (x).

A hujja dogara ne a kan maanar wata wanda aka samu aiki

Mun ayyana x (sabani) a cikin wasu kananan unguwa da wani batu x Δh _0. Zã Mu nũna da aiki darajar da shi, kuma a cikin aya x samu increment na wani ba aiki. Idan Δh - shawara incremented, sabon shawara - wannan x ₀ + Δx = x, da darajar da wannan aiki ga wani ba tamanin da shaida (x) ne daidai Zunubi (x ₀ + Δx), da aiki da darajar a wata takamaiman ma'ana (x ₀₎ ne kuma a san .

Yanzu dole mu Δu = Zunubi (x ₀ + Δh) -Sin (x ₀₎ - samu increment aiki.

Bisa ga dabara na ba tare da ware Naira Miliyan Xari biyu unequal kusassari za mu maida bambanci Δu.

Δu = Zunubi (x ₀₎ · cos (Δh) + cos (x ₀₎ · Zunubi (Δx) debe Zunubi (x ₀₎ = (cos (Δx) -1 ) · Zunubi ( x ₀₎ + cos (x ₀₎ · Zunubi (Δh).

Yi permutation sharuddan harhada farko zuwa na uku Zunubi (x _0), dauka daga cikin na kowa factor - ba tare da - da baka. Mun samu a cikin magana cos bambancin (Δh) -1. Yana bar canza ãyã a gaban zance da baka. Sanin abin da aka da 1-cos (Δh), mu yi canji da kuma samun Sauki magana Δu, to, wanda aka raba da Δh.
Δu / Δh za siffar: cos (x ₀₎ · Zunubi (Δh) / Δh 2 · Zunubi ² (0.5 x Δh) · Zunubi (x ₀₎ / Δh. Wannan shi ne rabo na increment na aiki da kudin shiga ga increment da shaida.

Ya zauna a sami iyaka da rabo samu ta hanyar da mu a lokacin Lim Δh, jinyar da sifili.

An sani cewa iyaka Zunubi (Δh) / Δx ne daidai da 1, a karkashin yanayin. Kuma da magana 2 · Zunubi ² (0.5 x Δh) / Δh a cikin sakamakon Naira Miliyan Xari musamman canje zuwa samfurin dauke da matsayin farko multiplier ƙwarai iyaka: da numerator na sulusi da murabba'i da znemenatel raba ta 2, da square na ba tare da maye gurbin samfurin. Ga yadda ake yi:
(Zunubi (0,5 · Δx) / (0,5 · Δx)) · Zunubi (Δx / 2).
A iyaka na wannan magana a lokacin da Δh o ƙarin sifili, zai zama daidai da yawan sifili (0 yawaita by 1). Sai dai itace cewa da iyaka da rabo Δy / Δh ne cos (x ₀₎ · 1-0, wannan ne cos (x _0), da magana daga wanda yake mai zaman kanta da Δh jinyar zuwa 0. A ƙarshe: da wanda aka samu daga cikin ba tare da na ko ta wane hali ne daidai x cosine na x, za a iya rubuta kamar: y '= cos (x).

A sakamakon dabara aka jera a kan tebur na san Kalam, inda duk na farko ayyuka

A warware matsaloli, inda ya gana da wanda aka samu daga cikin ba tare da, za ka iya amfani da dokoki na bambantawa da kuma shirye-sanya dabarbari na tebur. Ga misali: nemo wanda aka samu daga cikin sauki aiki y = 3 · Zunubi (x) -15. Mun yi amfani da na farko derivation dokoki kau na lamba factor ga alama na wanda aka samu da kuma lissafi da wanda aka samu m lamba (wanda shi ne sifili). Aiwatar da wani ba tare da tebur darajar da wanda aka samu daga cikin kwana x daidai cos (x). Sami amsar: y '= 3 · cos (x) -O. Wannan wanda aka samu, bi da bi, shi ne kuma wani na farko aiki y = H · cos (x).

The wanda aka samu daga ba tare da Squared na da wani misãli

A lissafi na magana (Zunubi ² (x)) 'dole ne ka tuna da yadda bambanta hadaddun aiki. Saboda haka, ² = Zunubi (x) - shi ne mai ikon aiki a matsayin ba tare da Squared. Its shaida ne kuma mai trigonometric aiki, wani hadadden shawara. A sakamakon a cikin wannan yanayin ne ta daidaita da samfurin na farko multiplier ne square da hadaddun wanda aka samu da shaida, da kuma na biyu - da wanda aka samu daga cikin ba tare da. Ga mulkin for bambance aiki na wani aiki: (u (v (x))) 'yana (u (v (x)))' · (v (x)) '. Zancen na v (x) - wani hadadden shaida (ciki aiki). Idan ba aiki "y daidai da ba tare da Squared x", sa'an nan da wanda aka samu da wannan kumshin aiki ne y '= 2 · Zunubi (x) · cos (x). A samfurin na farko multiplier ninki biyu - wanda aka samu da aka sani karuwa da sauri aiki, da kuma cos (x) - wanda aka samu sinus hadaddun shawara na quadratic aiki. A karshe sakamakon za a iya canza ta yin amfani da dabara na trigonometric ba tare da na biyu kwana. A: A wanda aka samu shi ne Zunubi (2 · x). Wannan dabara ne sauki tuna, shi ne sau da yawa amfani da wani tebur.