# How to differentiate this function to find f'(7)?

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Suppose that f(x) is a differentiable function such that f(7+h)=2/(h+1) and that f(7)=2. Then f'(7) = ???

The answer is -2, I'm just not sure how to reach it.

Suppose that f(x) is a differentiable function such that f(7+h)=2/(h+1) and that f(7)=2. Then f'(7) = ???

The answer is -2, I'm just not sure how to reach it.

##### 1 Answer

May 16, 2018

See below

#### Explanation:

We use the definition of the derivative

For the given function, we have

**Alternative**

You could also simply recognize that the function is simply

so that

I guess from the way the problem is worded, though, that a calculation using the definition of the derivative is really being sought here.