what is the derivative of y=7csc4x?

Question

johnweldon1993 · Answer

use the chain rule...you know you can take 7 out of the equation since It is a constant multiple...so firstly...what is the derivative of csc?

anonymous · Answer

would it be cscxcotx?

johnweldon1993 · Answer

it would be -csc(x)cot(x) right? don't forget the '-' but yes....

now THAT is the derivative of csc(x)...but what YOU have...is csc(4x) so that cannot be correct...yet

so far you have

7 * -csc(4x)(cot(4x) * d/dx 4x

which you know is 4

so altogether you have

7 * -csc(4x)cot(4x) * 4

which comes out to

28 (-csc(4x)(cot(4x))

or

-28(csc(4x)(cot(4x))

anonymous · Answer

oh yes, i had forgotten the '-'

johnweldon1993 · Answer

And there you go :) you see what I did correct?

anonymous · Answer

yes, thanks

johnweldon1993 · Answer

Also ...an EASY way to remember which derivatives has a '-' in them

d/dx cos(x) = -sin(x)
d/dx cot(x) = -csc²(x)
d/dx csc(x) = -cot(x)csc(x)

see how each terms that starts with a 'c' has a NEGATIVE derivative?

Cos
Cot                  = all negative derivatives :)
Csc

anonymous · Answer

oh yea, thanks again

johnweldon1993 · Answer

anytime!