Find the Derivative of the Functions y = 2x ^ 3-3x ^ 4 + 19

In order to find the derivative of the function y = 2x ^ 3 – 3x ^ 4 + 19, we first of all recall the property of the derivative of the sum and the difference:

(u + v) ‘= u’ + v ‘;

(u – v) ‘= u’ – v ‘.

So, we apply the property and get:

y ‘= (2x ^ 3 – 3x ^ 4 + 19)’ = (2x ^ 3) ‘- (3x ^ 4)’ + 19 ‘.

Next, we will apply the formula to find the derivative of the exponential function:

(x ^ n) ‘= n * x ^ (n – 1),

And also apply:

(cu) ‘= cu’;

c ‘= 0.

and we get:

(2x ^ 3) ‘- (3x ^ 4)’ + 19 ‘= 2 * 3x ^ 2 – 3 * 4x ^ 3 + 0 = 6x ^ 2 – 12x ^ 3.

Answer: y ‘= 6x ^ 2 – 12x ^ 3.