Final answer:
The derivative of the given function can be found using the power rule of differentiation. Applying the rule to each term of the function, we can determine the derivative of f(x) as 616x⁴³ + 42x⁶ - 8x³ + 19. Therefore, the derivative of f(x) is f'(x) = 616x⁴³ + 42x⁶ - 8x³ + 19.
Step-by-step explanation:
To find the derivative of the function f(x) = 14x⁴⁴ + 6x⁷ - 2x⁴ + 19x - 7, we can apply the power rule of differentiation. The power rule states that if we have a term of the form ax^n, the derivative is given by nx^(n-1).
Applying the power rule to each term of f(x), we get:
- The derivative of 14x⁴⁴ is 44(14)x^(44-1) = 616x⁴³.
- The derivative of 6x⁷ is 7(6)x^(7-1) = 42x⁶.
- The derivative of -2x⁴ is 4(-2)x^(4-1) = -8x³.
- The derivative of 19x is 19.
- The derivative of -7 is 0 since it is a constant.
Therefore, the derivative of f(x) is f'(x) = 616x⁴³ + 42x⁶ - 8x³ + 19.