derivative!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Question

Answer 1

Given that f(z) = (8z + e^(-z^2))^6

Differentiating on both sides we get,

f'(z) = d/dz (8z + e^(-z^2))^6                     

      = 6(8z + e^(-z^2))^5 d/dx(8z + e^(-z^2))                [Since d/dz(z^a) = az^(a-1)]

      = 6(8z + e^(-z^2))^5  (8 + e^(-z^2) d/dz(-z^2) )      [Since d/dz(az) = a, d/dz(e^z) = e^z]

      = 6(8z + e^(-z^2))^5  (8 + e^(-z^2) (-2z))               [Since d/dz(z^a) = az^(a-1)]

      = 6(8z + e^-z^2)^5  (8 -2z e^-z^2)

Therefore f'(z) = 6(8z + e^-z^2)^5  (8 -2z e^-z^2)