Math: Derivatives
posted by Nick on .
Use the shortcut rules to mentally calculate the derivative of the given function
f(x) = −x + (3/x) + 1
After deriving it, I got
1+(0/1)+0= 1
But this answer is wrong, and I don't know why.
Thank You

The derivative of f(x) is
13/x²
Don't know how you got 1, or what the question really is. 
How did you get the answer? I don't quite understand. Thanks

If f(x)=g(x)+h(x), then
linearity gives
f'(x)=g'(x)+h'(x)
so
f(x)=x + (3/x) + 1
f'(x)= (x)' + (3/x)' + (1)'
=1 3/x² + 0
=1 3/x²
The second term is obtained by the power rule:
d(1/x)/dx = 1/x²