Derivatives of sin-1(x), cos-1(x) and tan-1(x)

Revision Points - Derivatives of sin-1(x), cos-1(x) and tan-1(x)

Definition and Understandings

• Inverse trigonometric functions are functions that undo the basic trigonometric functions (sin, cos, tan).
• The inverse of sin is sin-1(x), sometimes written as arcsin(x).
• The inverse of cos is cos-1(x), or arccos(x).
• The inverse of tan is tan-1(x), or arctan(x).

Derivatives

• Understand how to find the derivative of these inverse trig functions.
• The derivative of sin-1(x) is 1/sqrt(1-x²).
• The derivative of cos-1(x) is -1/sqrt(1-x²).
• The derivative of tan-1(x) is 1/(1+x²).

Using the Derivatives

• Use these derivatives to find the gradient of a tangent line to the graph at a given point.
• Apply chain rule when doing the derivative of more complex functions involving sin-1(x), cos-1(x) or tan-1(x).
• Skills in differentiation are critical across other sections of Core Pure Maths, including further differentiation and integration topics.

Applications and Practice

• Consider real-life examples where these derivatives are used, such as in engineering and physics problems.
• Apply these derivatives to solve problems and improve understanding.
• Regular practice with a variety of problems will help to reinforce knowledge and provide confidence in using these derivatives.

Remember, a good understanding of these inverse trigonometric functions and their derivatives is necessary for success with Core Pure Maths. Keep practicing, and ensure clarity in each step of the process while differentiating these functions.