Ummmm help please :(. Let f(X)= (-5x)/sin(X)+cos(X).

I assume this is

f(x)= (-5x)/ [ sin(x)+cos(x)  ]   .....if so.....we can write it as

(-5x) [ sin (x) + cos(x)]^(-1)    ......so.....using the product and chain rules, we have.....

f ' (x) =  -5 [ sin (x) + cos(x)]^(-1)   +  (5x)[sin (x) + cos(x)]^(-2)  (cos(x) - sin(x) ]

So    f '  (2pi) =

-5 [ sin (2pi) + cos(2pi)] ^(- 1)  + (5*2pi) [ sin(2pi) + cos(2pi)]^(-2) ( cos(2pi)  - sin (2pi) ]  =

-5  [ 0 + 1]^(-1)  + (5*2pi) [ 0 + 1^(-2) ( 1 - 0)  =

-5 + 5*2pi  =

5 [2pi - 1]  =  about 26.416

Thanks to the guest for pointing out my earlier error....!!!!

Wouldn't it actually be 5[2pi-1]?

Thanks, guest....I made a boo-boo there....let me correct that....!!!