Ib nrab derivatives thiab txuas ntxiv. Yog txoj haujlwm f: R → R yog diifierentiable, ces f yog txuas ntxiv. cov derivatives ib nrab ntawm ib txoj haujlwm f: R2 → R. f: R2 → R xws li fx(x0, y0) thiab fy(x0, y0) tab sis f tsis tas li ntawm (x0, y0).
Yuav ua li cas koj thiaj paub yog tias ib feem derivative txuas ntxiv?
Let (a, b)∈R2. Tom qab ntawd, kuv paub tias ib nrab derivatives muaj thiab fx(a, b)=2a + b, thiab fy(a, b)=a + 2b. Txhawm rau ntsuas qhov txuas ntxiv, lim(x, y) →(a, b)fx(x, y)=lim(x, y) →(a, b) 2x + y=2a + b=fx(a, b).
Dab tsi yog ib feem derivatives?
1.1.
V (x)=(x 1 + x 2) 2 Rau tag nrho cov Cheebtsam ntawm ib vector x, muaj ib qho kev sib txuas tsis tu ncua V(x); thaum x=0, V(0)=0 tab sis tsis yog rau x ≠ 0, peb muaj V(x) > 0, piv txwv li, thaum x1=−x 2, peb muaj V(x)=0, yog li V(x) tsis zoo meej muaj nuj nqi thiab yog semipositive definite function.
Puas yog qhov sib txawv ntawm ib feem cuam tshuam txuas ntxiv?
Ib kab hauv qab: muaj ib feem derivatives yog qhov tsis muaj zog zoo nkaujvim nws tsis tau lees paub txuas ntxiv! Kev sib txawv (muaj nyob ntawm qhov kwv yees zoo linear) yog qhov muaj zog ntau dua.
Puas sib txawv txhais tau tias muaj ib feem ntawm cov khoom siv?
Qhov sib txawv theorem hais tias txuas ntxiv ib feem derivatives txaus rau ib txoj haujlwm kom sib txawv. …Kev sib tham ntawm qhov sib txawv theorem tsis muaj tseeb. Nws yog qhov ua tau rau qhov kev ua haujlwm sib txawv kom muaj cov khoom siv tsis tu ncua.
