(a) Use the Quotient Rule to differentiate the function f(x)=tan(x)-1/sec(x). f'(x)= (b) Simplify the expression for f(x) by writing it in terms of sin(x) and cos(x), the find f'(x).

(c) Are your answers to part (a) and (b) equivalent?

For part (a) (which I got correct), I got f'(x)=-sin(x)tan(x)+sec(x)+sin(x)
I got part (b) wrong and I am certain it is a simple thing I am overlooking, but if someone could show me, I would appreciate it.

For part (c) I knew they were equivalent, and the answers is yes.

(a) sin(x) + cos(x)

(b) sin(x) + cos(x)

(c) Both answers are equivalent

Step-by-step explanation:

(a) The given function is:

According to the quotient rule:

Applying the quotient rule:

This can be simplified to:

(b) Simplifying in terms of sin(x) and cos(x):

(c) As proven above, both answers are equivalent.

option a.

step-by-step explanation:

if you look closely at the graph, we can notice that the function is not defined at two different points.

if you look at functions b and c, you will notice that both functions are not defined at just one point. the function b is not defined at x= -5/2 and function c is not defined at x=-5. both options are discarded, given that our function should not be defined at two fiferent points.

now, if you look closely at the graph you will notice that the function sketched is not defined at x=5 and x=-2.