Question

If f(x) = (x² -3)⁴, then f'(1) =???

Answer 1

To find f'(1), we need to take the derivative of the function f(x) = (x² - 3)⁴ and evaluate it at x = 1. Using the chain rule, we can differentiate the function and substitute x = 1 to calculate f'(1) = -32.

Step-by-step explanation:

To find f'(1), we need to take the derivative of the function f(x) = (x² - 3)⁴ and evaluate it at x = 1.

Using the chain rule, we can differentiate the function as follows:

f'(x) = 4(x² - 3)³ * 2x

Substituting x = 1 into the derivative equation, we get:

f'(1) = 4(1² - 3)³ * 2(1)

Simplifying the expression, we have:

f'(1) = 4(-2)³ * 2

Calculating further, we get:

f'(1) = -32

Therefore, f'(1) = -32.