Question

find f prime of x if f(x) = x^2-x

I understand that f prime (x)= 2x i just dont understand how to work the -x

Answer 1

\[f(x) = x^2-x\]\[f'(x) = \text{derivative of \(x^2\) - derivative of \(x\)}\]

Answer 2

Exactly.
The derivative of x2 is 2x how do i find out the derivative of x

Answer 3

\[x = x^1\]

Answer 4

\[x^0 = 1, \,x\ne 0\]

Answer 5

Going back to the limit definition of the derivative,
\[\frac{d}{dx}[x] = \lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h} = \lim_{h\rightarrow 0}\frac{x+h-x}{h} = \lim_{h\rightarrow 0}\frac{h}{h} = 1\]

Answer 6

so the answer is 2x-1 or just 2x?