Question

Find the derivative of f(x) = 7/x at x = 1.

Answer 1

plug in 1 for x.

the derivative of a constant equals zero. always.

Answer 2

oh heck no

Answer 3

are you supposed to do this by hand, or can you use the fact that if
\[f(x)=\frac{1}{x}\] then
\[f'(x)=-\frac{1}{x^2}\]?

Answer 4

my bad, it's a derivative of a function, sorry abt that.

Answer 5

i guess i was asking if you had to find this using the definition, or if you can use what you know about derivatives, either by the power rule or from the definition

Answer 6

quick answer is if \(f(x)=\frac{7}{x}\) then \(f'(x)=-\frac{7}{x^2}\) and so \(f'(1)=-7\)

Answer 7

slow answer is computing
\[\lim_{x\to 1}\frac{\frac{7}{x}-7}{x-1}\]