Question

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determine the fourth derivative of given function ​

Answer 1

Answer: 2520t³-144

Given:

$h(t)=3t^{7}-6t^{4}+8t^{2} -12t+18$

Formula used:

$x^{n}=nx^{n-1}$

Explanation:

First derivative,

$h'(t)=7*3t^{6}-6*4t^{3}+2*8t^{1} -12\\ h'(t)=21t^{6}-24t^{3}+16t -12$

Second derivative,

$h''(t)=21*6t^{5}-24*3t^{2}+16\\h''(t)=126t^{5}-72t^{2}+16$

Third derivative,

$h'''(t)=126*5t^{4}-72*2t^{1}\\h'''(t)=630t^{4}-144t^{}$

Fourth derivative,

$h^{4} (t)=630*4t^{3}-144t^{1}\\ h^{4} (t)=2520t^{3}-144$