How do you find the derivative of #y=ln(t)/t^2#?
To solve this problem, one must use the quotient rule.
The quotient rule for derivatives states the following:
#(d/dx) [(u(x))/(v(x))] = [u'(x)v(x) - u(x)v'(x)]/[v^2(x)]#.
In other words, the derivative of the quotient is equal to:
The derivative of the numerator function times the original denominator function, minus the product of the original numerator function and the derivative of the denominator function, all divided by the square of the original denominator function. Note that this only works at locations where
#v(x) != 0#
Now, for the particular problem in question, we have
The derivative of the function
Using our above formula for the quotient rule, we arrive at, for all