Posted by **Nick** on Sunday, April 8, 2012 at 2:56pm.

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

- Math: Derivatives -
**MathMate**, Sunday, April 8, 2012 at 3:51pm
The derivative of f(x) is

-1-3/x²

Don't know how you got -1, or what the question really is.

- Math: Derivatives -
**Nick**, Sunday, April 8, 2012 at 8:20pm
How did you get the answer? I don't quite understand. Thanks

- Math: Derivatives -
**MathMate**, Monday, April 9, 2012 at 4:01pm
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

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