What are the derivatives of the following functions as specified?

Question

Find the derivatives of the following functions as specified

a. 𝑦 = cos²𝑥 , 𝑦′′′

b. 𝑦 = 𝑥²/2𝑥 + 1 , 𝑦′′′

c. 𝑦 = = (𝑥² − 4) ^2/3 , 𝑦′′

d. 𝑦 = 𝑒^{𝑥^2} , 𝑦′′′

Answer 1

c. y= (x^2-4)^2/3

y' = (2/3)(x^2-4)^-1/3(2x)

= (4x/3)/(x^2-4)^1/3

= 4x/3(x^2-4)^1/3