Find the third-order derivative of the function Y = 3x ^ 4 + 5x ^ 5-7x + 9.

To find the derivative of a function, you need to use the table of derivatives:

x ‘= 1;

C ‘= 0, C = const;

(x ^ n) ‘= n * x ^ (n – 1).

Let’s find the first derivative of the given function:

y ‘= (3x ^ 4 + 5x ^ 5 – 7x + 9)’ = 3 * 4 * x ^ (4 – 1) + 5 * 5 * x ^ (5 – 1) – 7 * 1 + 0 = 12x ^ 3 + 25x ^ 4 – 7.

Let’s find the second derivative of the given function:

y ” = (12x ^ 3 + 25x ^ 4 – 7) ” = 12 * 3 * x ^ (3 – 1) + 25 * 4 * x ^ (4 – 1) – 0 = 36x ^ 2 + 100x ^ 3.

Let’s find the third derivative of the given function:

y ” ‘= (36x ^ 2 + 100x ^ 3)’ ” = 36 * 2 * x ^ (2 – 1) + 100 * 3 * x ^ (3 – 1) = 72x + 300x ^ 2.