12.3: Differentiation of Trig Functions

Derivatives of the Trigonomic Functions

derivative of sin(x) = cos(x)
derivative of cos(x) = -sin(x)

*We can use these to find the derivatives of the other trig functions which are:

derivative of tan(x) = sec^2(x)
derivative of cot(x) = -csc^2(x)
derivative of sec(x) = sec(x) tan(x)
derivative of csc(x) = -csc(x) cot(x)

Examples

• Find the derivative of sin(7x+3)

• Use the chain rule to find the derivative of the function.

  derivative of the outside function while the inside stays the same times the
  derivative of the inside.

  Answer: cos(7x+3) (7)

• Find the derivative of e^csc(x)

• Follow the steps that we learned in a earlier lesson

  e to the something times the derivative of the
  something

  Answer: (e^csc(x)) (-csc(x) cot(x))

Check out this site for more practice problems:

http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/trigderivdirectory/TrigDerivatives.html

KJ you are up next. I couldn't tell you which one because it is not even on the TWS.

"He who has no Christmas in his heart will never find Christmas under a tree."