Differentiating Trigonometric Functions


Back to Differentiation Topics Page


Now you will be differentiating other trigonemtric functions. Let's start with tanx, cotx, secx and cosecx.

You may be asked on how to prove these formulas. Here are the proofs of how you could prove the derivatives of tanx and secx:

Example 1:

Example 1
Answer 1
Example 2
Answer 2

Example 2:

Example 1
Answer 1
Example 2
Answer 2

Note: The proof for the derivative of cotx is very similar to the derivative of tanx and the proof for the derivative of cosecx is very similar to the derivative of secx. You can do those proofs for practice.

The next set of formulas are the derivatives for the inverse sin, cos and tan functions:

You can use the formula dy/dx=1/dx/dy to prove these formulas. An example of these proofs is the proof for the derivative of arctanx:

Example 3:

Example 1
Answer 1
Example 2
Answer 2

The following examples use the formulae from above:

Example 4:

Example 1
Answer 1
Example 2
Answer 2

Practice Question:





Image