I'm trying to resolve a derivate. the derivate of 1/x of f(2). i get ((1/(2+deltax))-1/2)/delta. But i really don't know how to do the Least common multiple of (1/(2+deltax)) - 1/2.
Let's get the derivative, first.....then, we can "plug in"
lim(Δx →0) [1/(x +Δx) - 1/x]/Δx =
lim(Δx →0) [x/[x(x +Δx)] - (x +Δx)/[x(x +Δx)]]/Δx =
lim(Δx →0) [x - (x +Δx)]/(Δx[x(x +Δx)]) =
lim(Δx →0) [-Δx]/(Δx[x(x +Δx)]) =
lim(Δx →0) -1/[x(x +Δx)]=
lim(Δx →0) -1/[x2 +xΔx] .....now, take the limit = -1/[x2 + 0] =
-1/x2
And evaluating this at x = 2, we have
-1/22 = -1/4
Note..you could go back and substitute "2" for "x" in the limit stuff....you should arrive at the same answer without having to substitute at the end....!!!
Let's get the derivative, first.....then, we can "plug in"
lim(Δx →0) [1/(x +Δx) - 1/x]/Δx =
lim(Δx →0) [x/[x(x +Δx)] - (x +Δx)/[x(x +Δx)]]/Δx =
lim(Δx →0) [x - (x +Δx)]/(Δx[x(x +Δx)]) =
lim(Δx →0) [-Δx]/(Δx[x(x +Δx)]) =
lim(Δx →0) -1/[x(x +Δx)]=
lim(Δx →0) -1/[x2 +xΔx] .....now, take the limit = -1/[x2 + 0] =
-1/x2
And evaluating this at x = 2, we have
-1/22 = -1/4
Note..you could go back and substitute "2" for "x" in the limit stuff....you should arrive at the same answer without having to substitute at the end....!!!