Wie unterscheidet man f (x) = (sinx) / (sinx-cosx) anhand der Quotientenregel?

Antworten:

Die Antwort ist:

#f '(x) = - cosx (sinx + cosx) / (1-sin2x) #

Erläuterung:

Die Quotierungsregel besagt:

#a (x) = (b (x)) / (c (x)) #

Dann:

#a '(x) = (b' (x) * c (x) -b (x) * c '(x)) / (c (x)) ^ 2 #

Ebenso für #f (x) #:

#f (x) = (sinx) / (sinx-cosx) #

#f '(x) = ((sinx)' (sinx-cosx) -sinx (sinx-cosx) ') / (sinx-cosx) ^ 2 #

#f '(x) = (cosx (sinx-cosx) -sinx (cosx - (- cosx))) / (sinx-cosx) ^ 2 #

#f '(x) = (cosxsinx-cos ^ 2x-sinxcosx-sinxcosx) / (sinx-cosx) ^ 2 #

#f '(x) = (- sinxcosx-cos ^ 2x) / (sinx-cosx) ^ 2 #

#f '(x) = - cosx (sinx + cosx) / (sinx-cosx) ^ 2 #

#f '(x) = - cosx (sinx + cosx) / (sin ^ 2x-2sinxcosx + cos ^ 2x) #

#f '(x) = - cosx (sinx + cosx) / ((sin ^ 2x + cos ^ 2x) -2sinxcosx) #

#f '(x) = - cosx (sinx + cosx) / (1-sin2x) #