Please verify my answer

[CHiMER4]

Find the derivative of f(x)=1/(2-x) using the definition of derivatives (first principle)

I got f'(x)= (-1)/(2(√(2-x)^3))
Is there supposed to be a negative 1 ?
If there isn't may you please show me where my mistake may be

 

[lev888]

Find the derivative of f(x)=1/(2-x) using the definition of derivatives (first principle)

I got f'(x)= (-1)/(2(√(2-x)^3))
Is there supposed to be a negative 1 ?
If there isn't may you please show me where my mistake may be

Please post your solution.

 

[CHiMER4]

 

[tkhunny]

Now, you tell us if that negative sign should be there.

 

[Dr.Peterson]

View attachment 28579

On the third line there is a missing pair of parentheses. Fix that, and everything that follows.

 

[CHiMER4]

Now, you tell us if that negative sign should be there.

I got it by taking (2-x)-(2-x+h)=-h in lines 5 and 6

 

[CHiMER4]

On the third line there is a missing pair of parentheses. Fix that, and everything that follows.

I'm sorry, but where should the parentheses go .

Should it be in the first fraction, in the numerator?

 

[Dr.Peterson]

I'm sorry, but where should the parentheses go .

Should it be in the first fraction, in the numerator?

When you replace x with x+h, there must be parentheses around (x+h). Your are subtracting the entire quantity from 2.