Answer:
d(f(t))/dt = –56/(t^8) – (5/6)/t^(7/6) + 12t^3 – 2t + (1/3)t^(2/3))
Step-by-step explanation:
To find the derivative of f(t), we have to find the derivative of each component of the function to make it easier.
d(8/(t^7))/dt = d(8xt^-7)/dt = –7 x 8 x t^-8 = –56t^-8 = -56/(t^8)
d(5/(t^(1/6)))/dt = –(1/6) x 5 x t^(-7/6) = –(5/6)/t^(7/6)
d(3t^4)/dt = 4 x 3 x t^3 = 12t^3
d(t²)/dt = 2t
d(t^⅓)/dt = ⅓t^(-2/3) = (1/3)t^(2/3))
d(12)/dt = 0.
Therefore,
d(f(t))/dt = –56/(t^8) – (5/6)/t^(7/6) + 12t^3 – 2t + (1/3)t^(2/3))
