Paano mo naiiba ang y = x + ((x + sin ^ 2x) ^ 3) ^ 4?

Sagot:

#y '= 1 + 12 (x + sin ^ 2 (x)) ^ 11 (1-2sin (x) cos (x)) #

Paliwanag:

Nalutas ang problemang ito gamit ang tuntunin ng kadena:

# d / dx f (g (x)) = f '(g (x)) * g' (x) #

#y = x + ((x + sin ^ 2 (x)) ^ 3) ^ 4 = x + (x + sin ^ 2 (x)) ^ 12 #

Pagkuha ng hinangong:

# (dy) / dx = d / dx x + d / dx (x + sin ^ 2 (x)) ^ 12 #

# = 1 + 12 (x + sin ^ 2 (x)) ^ 11 * (d / dx (x + sin ^ 2 (x))) #

# = 1 + 12 (x + sin ^ 2 (x)) ^ 11 * (d / dx x + d / dx sin ^ 2 (x)

# = 1 + 12 (x + sin ^ 2 (x)) ^ 11 * (1 + 2sin (x) (d / dx sin (x)

# = 1 + 12 (x + sin ^ 2 (x)) ^ 11 (1 - 2sin (x) cos (x)) #