1.

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Solution

Given :-

  • h(t) = 3t^7 - 6t⁴ + 8t³ - 12t +18

Find :-

  • Fourth derivative of given FUNCTION Or h""(t).

Explanation

Using Formula

★ d(a^n)/da = n a^(n-1)

★ dn/dx = 0 , where n = CONSTANT

Now, differentiate first with respect to t

==> h'(t) = 7*3t^6 - 6*4t³ + 8*3t² - 12 + 0

==> h'(t) = 21t^6 - 24t³ + 24t² - 12

Again, differentiate

==> h"(t) = 21*6t^5 - 24*3t² + 24*2t - 0

==> h"(t) = 126t^5 - 72t² + 48t

again, differentiate

==> h"'(t) = 126*5t⁴ - 72*2t + 48

==> h"'(t) = 630t⁴ - 144t + 48

Again, differentiate

==>h""(t) = 630*4t³ - 144

==> h""(t) = 2520t³ - 144

Hence

  • Fourth differentiate will be = (2520t³ - 144)

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