How to find the derivative function of #g(x) = 3/(x-2)#? f(x)= f(x+h)-f(x) / h

Answer 1

I guess you want the derivative of #g(x)# using your definition of derivative (for #f(x)# in your question).
The complete definition is:
#lim_(h->0)(f(x+h)-f(x))/h=f'(x)#
and so:

hope it helps

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Answer 2

The derivative function of g(x) = 3/(x-2) can be found using the limit definition of the derivative. By applying the formula f'(x) = lim(h->0) [f(x+h) - f(x)] / h, we can calculate the derivative of g(x) as follows:

f'(x) = lim(h->0) [3/(x+h-2) - 3/(x-2)] / h

Simplifying further:

f'(x) = lim(h->0) [(3(x-2) - 3(x+h-2)) / ((x+h-2)(x-2))] / h

Expanding and canceling terms:

f'(x) = lim(h->0) [-3h / ((x+h-2)(x-2))] / h

Simplifying:

f'(x) = lim(h->0) [-3 / (x+h-2)(x-2)]

Taking the limit as h approaches 0:

f'(x) = -3 / (x-2)^2

Therefore, the derivative function of g(x) = 3/(x-2) is f'(x) = -3 / (x-2)^2.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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