Find the first four derivatives :

Question

i.) y = x^-3 + 3x^3 + 6x^2
ii.) y = - 3/x
iii.) y = 2cos2x

Answer 1

i.) y = x^-3 + 3x^3 + 6x^2

First derivative:
y' = -3x^-4 + 9x^2 + 12x

Second derivative:
y'' = 12x^-5 + 18x

Third derivative:
y''' = -60x^-6

Fourth derivative:
y'''' = 360x^-7

ii.) y = -3/x

First derivative:
y' = 3/x^2

Second derivative:
y'' = -6/x^3

Third derivative:
y''' = 18/x^4

Fourth derivative:
y'''' = -72/x^5

iii.) y = 2cos2x

First derivative:
y' = -4sin2x

Second derivative:
y'' = -8cos2x

Third derivative:
y''' = 16sin2x

Fourth derivative:
y'''' = 32cos2x