Β 
VIEW IN FULL SCREEN

OCR A-level Maths Differentiation of trigonometric functions

Differentiation of trigonometric functions

This page covers the following topics:

1. Differentiating trigonometric functions
2. Differentiating trigonometric reciprocals
3. Differentiating trigonometric functions with the chain rule
4. Differentiating trigonometric functions without the chain rule

Equations involving trigonometric functions can be differentiated using the basic rules of differentiation by using the following results: d(sinx)/dx = cosx, d(cosx)/dx = βˆ’sinx and d(tanx)/dx = secΒ²x.

Differentiating trigonometric functions

Equations involving trigonometric reciprocals can be differentiated using the basic rules of differentiation by using the following results: d(cotx)/dx = βˆ’cosecΒ²x, d(secx)/dx = secxtanx and d(cosecx)/dx = βˆ’cosecxcotx.

Differentiating trigonometric reciprocals

The Chain rule can be applied to differentiate equations involving trigonometric functions using the results of their derivatives.

Differentiating trigonometric functions with the chain rule

All differentiation rules can be used with the results for the derivatives of trigonometric functions to differentiate equations involving trigonometric functions.

Differentiating trigonometric functions without the chain rule

1

Find a function for the slope for the given graph.

Find a function for the slope for the given graph.

2

Differentiate the following function: g(x) = secΒ²xcosx/tanx.

Differentiate the following function: g(x) = secΒ²xcosx/tanx.

3

Prove that the derivative of cotx is βˆ’cosecΒ²x.

Prove that the derivative of cotx is βˆ’cosecΒ²x.

4

Differentiate the following function: f(x) = 1/tanx + secx.

Differentiate the following function: f(x) = 1/tanx + secx.

5

Find the derivative of y = 8tanΒ³x.

Find the derivative of y = 8tanΒ³x.

End of page

Β