Question 6.33: Find the first, second and third derivatives of the followin......

(a) C = 100(1 − e^Y)

C = 100 − 100e^Y\\\frac {dC}{dY} = − 100(e^Y)\\\frac {d²C}{dY²} = − 100(e^Y)\\\frac {d³C}{dY³} = − 100e(^Y)

(b)TC = 10 + lnQ

(c) y = 4e^{2.5x}

y = 4e^{2.5x}\\\frac {dy}{dx} = 4(2.5e^{2.5x}) = 10e^{2.5x}\\\frac {d²y}{dx²} = 10(2.5e^{2.5x}) = 25e^{2.5x}\\\frac {d³y}{dx³} = 25(2.5e^{2.5x}) = 62.5e^{2.5x}