7 to 42 Find the derivative of the function. h(t) = (t+ 1)2/3(2+2 - 1) 3 Here is the step-by-step explanation, verified by an educator: Step 1 of 3 Use the Product Rule to differentiate the given function. h' ( t ) = ( t + 1) 2/3 . # ( 2+2 - 1) 3 + ( 2+2 - 1) 3. 2 (t + 1) 2/3 Step 2 of 3 Use the Chain Rule. = (t + 1)2/3 . 3(2+2 - 1)2 . 2 (2+2 - 1) + (2t2 - 1)3 . 2(t + 1)-1/3 . 4 (t + 1) = (t + 1)2/3 . 3(2+2 - 1)2 . (4t) + (2+2 - 1) 3 . 2(t + 1)-1/3 . (1) Step 3 of 3 Multiply by the common denominator 3(t + 1)1/3 and simplify. = 12t(t + 1)2/3(2+2 - 1)2 + + 2 (2+2 - 1 ) 3 3 ( t + 1 ) 1 / 3 = 12t(t + 1)2/3(2+2 - 1)2 + 3(141)13 3(t+1)1/3 3(t+1)1/3 - 2(212 1)3+36t(1+1) (2+2 1)2 3(1+1)173 2(t2 -1)2 = 3 (t+1) 1/3 . (2t2 - 1) + 18t(t + 1)] 2(t2 -1)2 3(t+1)1/3 . (2t2 - 1 + 18+2 + 18t) = =(t+1)-1/3(2+2 - 1)2(20t2 + 18t - 1)