2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions

Remember the cheat sheet from the previous article on the derivatives of sin(x), cos(x), e^x, and ln(x)?

We previously focused on the first two equation on the list, but now we're going to expand what you know to the rest of the left side of the table. The same idea used before applies here as well!

Example: Find the derivative of f(x) = tan 2x.

Based on the model above, u = 2x.

f'(x) = 2sec^2 (2x).

Example: Find the derivative of f(x) = -cot x.

Be careful with signs! Make sure not to confuse the given sign (-) and the sign of the derivative (also -). They're not the same!

f'(x) = -[-csc^2 (x)]

f'(x) = csc^2 (x).