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### Section 3.12 : Higher Order Derivatives

1. Determine the fourth derivative of $$h\left( t \right) = 3{t^7} - 6{t^4} + 8{t^3} - 12t + 18$$

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Not much to this problem other than to take four derivatives so each step will show each successive derivative until we get to the fourth. The first derivative is then,

$h'\left( t \right) = 21{t^6} - 24{t^3} + 24{t^2} - 12$ Show Step 2

The second derivative is,

$h''\left( t \right) = 126{t^5} - 72{t^2} + 48t$ Show Step 3

The third derivative is,

$h'''\left( t \right) = 630{t^4} - 144t + 48$ Show Step 4

The fourth, and final derivative for this problem, is,

$\require{bbox} \bbox[2pt,border:1px solid black]{{{h^{\left( 4 \right)}}\left( t \right) = 2520{t^3} - 144}}$