Shortcuts hints for memorizing
I don’t like memorizing any more than anyone else. So I know that the derivative of sin x is cos x. But instead of memorizing derivative of cos x, I use the fact that cos is the COFUNCTION of the sin. I also know that DERIVATIVE OF COFUNCTIONS REQUIRE A ‘-1’ FACTOR. So to find the derivative of cos x, the cofunction is sin x. Now the derivative of the sin x is cos x. So the derivative of cos x is -1* cofunction of derivative of sin x or -1* cofunction of cos x or -sin x. Make sense?
This may seem like even more work, but it will prove useful as we explore the other four trig functions.
As a reference for derivatives please go to Thinkwell. Near the bottom on the left select RESOURCES. Then on the right window under LINKS select VISUAL CALCULUS. Under Tutorials select DERIVATIVES. The last heading at the bottom is Derivative of Functions. Finally, select A LIST OF DIFFERENTIAL FORMULAS. Focus please on and memorize #9, #11 & #13, no more. Notice how my idea above now works.
To find the derivative of csc x, knowing that the derivative of sec x is sec x tan x,
we just take -1*cofunctions or derivative of csc x is -csc x cot x!
0 comments