Kaj je derivat y = x ^ 2-5x + 10?

Odgovor:

# d / dx (x ^ 2 5x + 10) = 2x-5 #

Pravilo moči daje izpeljanko izraza oblike # x ^ n #.

# d / dx x ^ n = n * x ^ {n-1} #

Potrebovali bomo tudi linearnost derivata

# d / dx (a * f (x) + b * g (x)) = a * d / dx (f (x)) + b * d / dx (g (x)) #

in da je derivat konstante nič.

Imamo

#f (x) = x ^ 2 5x + 10 #

# d / dxf (x) = d / dx (x ^ 2 - 5x + 10) = d / dx (x ^ 2) - 5d / dx (x) + d / dx (10) #

# = 2 * x ^ 1-5 * 1 * x ^ 0 + 0 = 2x-5 #