Question

F(x)=9-x^(2 )find the derivative of function using 4 step rule

Answer 1

The derivative of function is F'(x) = -2x

Step-by-step explanation:

To find the derivative of the given function F(x) = 9 - x² using the 4-step rule, we'll follow a systematic approach.

Step 1: Identify the original function and label it as F(x) = 9 - x² .

Step 2: Apply the power rule, which states that the derivative of
`x^n` is
`\( nx^((n-1)) \)`. In this case, the derivative of -x² is -2x .

Step 3: The constant term 9 has no impact on the derivative, so it remains unchanged.

Step 4: Combine the results from Steps 2 and 3 to obtain the final derivative F'(x) = -2x .

In summary, the derivative of the function F(x) = 9 - x^2 is F'(x) = -2x . This means that for any given value of x , the rate of change of the original function is -2x.