How do I solve this using the TERM BY TERM method?

If f(x)= (2x^2 - 5x - 3) / (3-x)

find f'(-8).

2(-8)^2 = 2*64 = 128

-5(-8) = 40
-3 = -3 now add
-------------
165 = numerator

3 - (-8) = 11

so
165/11

that's f(-8), but we want f'(-8)

f(x) = -(2x+1)

To solve this using the TERM BY TERM method, you need to differentiate each term of the function separately and then simplify.

First, let's find the derivative of each term:

- Derivative of 2x^2: To find the derivative of 2x^2, you multiply the coefficient (2) by the exponent (2), giving you 4x.

- Derivative of -5x: To find the derivative of -5x, the derivative of x is simply 1, and the coefficient is -5. Thus, the derivative is -5.

- Derivative of -3: The derivative of a constant term is always zero.

So, the derivative of the function f(x) = (2x^2 - 5x - 3) / (3-x) term by term is:

f'(x) = (4x - 5) / (3-x)

Now, to find f'(-8), replace x with -8 in the derivative:

f'(-8) = (4(-8) - 5) / (3 - (-8))
= (-32 - 5) / (3 + 8)
= (-37) / (11)
= -37/11

Therefore, f'(-8) = -37/11.