M1函數的求導法及二階導數 c

1.a. y = 3e^x - 7

dy/dx = 3e^x, d^2ydx^2 = 3e^x


b. y = (1 + e^x)(1 - e^x) = 1 - e^2x

dy/dx = -2e^2x, d^2y/dx^2 = -4e^2x


c. y = (2 + e^x)^2 = 4 + 4e^x + e^2x

dy/dx = 4e^x + 2e^2x, d^2y/dx^2 = 4e^x + 4e^2x


2.a. y = e^5x - 4

dy/dx = 5e^5x, d^2y/dx^2 = 25e^5x


b. y = e^(-2x)

dy/dx = -2e^(-2x), d^2y/dx^2 = 4e^(-2x)


c. y = e^(x/2)/2 + e^(-x/2)

dy/dx = (1/2)(1/2)e^(x/2) - (1/2)e^(-x/2) = (1/4)e^(x/2) - (1/2)e^(-x/2)

d^2y/dx^2 = (1/8)e^(x/2) - (1/4)e^(-x/2)