What is the derivative of # y= 1/ (sinx+cosx)#?
Notice that your function is actually the quotient of two other functions, which means that you can use the quotient rule to determine its derivative.
More specifically, those two functions are
such that your function can be written as
Now, the quotient rule says that th derivative of a quotient of two functions is equal to
You also know that
and that the derivative of a constant is equal to zero
which means that you have
SIDE NOTE You could also use the reciprocal rule, which deals with the special case of