Question

The derivative of 1/x? I'm blanking on my simple rules here; thanks, actually thought of that right after i asked this whats the derivative of 1/x... i think its 1 but i could be completely wrong here; you'll still get the 10 points, thanks for the help if you can whats the derivative of f(x)= k/x and x/k where k is a constant

Answer 1

D(1/x)/dx= d(x^-1)/dx
= -x^-2

the derivatives of the two cases you mentioned is as follows:
(I) f(x)=k/x
d{f(x)}/dx= k×(-x^-2)
= -kx^-2

(ll) f(x)=x/k
d{f(x)}= d(x/k)/dx
= 1/k

you can just simply take out the constant from the derivative and multiply it to the final answer of the derivative of the given function.