Question

Find the second derivative of the algebraic function:
f(t)= (9t+2) ^ 2/3

Answer 1

Do you use the power rule or the chain rule?

Answer 2

You use the Chain Rule, with the Power Rule playing the role of the "outside" function. So \[f'(t)=\tfrac{2}{3}(9t + 2)^{-1/3}\cdot 9=6(9t + 2)^{-1/3}\].

Answer 3

Oops, I just saw that you wanted \[f''(t)\] To calculate this, just differentiate again using the same procedure. So \[f''(t)=-18(9t + 2)^{-4/3}\]

Answer 4

Ohh okay that makes sense! thank you