IB DP Maths: AA HL复习笔记5.8.4 Differentiating Further Functions

This Revision Note focuses on the results and derivations of results involving the less common trigonometric, exponential and logarithmic functions.  As with any function, questions may go on to ask about gradients, tangents, normals and stationary points.

What are the reciprocal trigonometric functions?

• Secant, cosecant and cotangent and abbreviated and defined as

What are the derivatives of the reciprocal trigonometric functions?

How do I show or prove the derivatives of the reciprocal trigonometric functions?

What do the derivatives of reciprocal trig look like with a linear functions of x?

• 
  • These are not given in the formula booklet
    • they can be derived from chain rule
    • they are not essential to remember

What are the inverse trigonometric functions?

• arcsin, arccos and arctan are functions defined as the inverse functions of sine, cosine and tangent respectively

What are the derivatives of the inverse trigonometric functions?

How do I show or prove the derivatives of the inverse trigonometric functions?

What do the derivative of inverse trig look like with a linear function of x?

• These are not in the formula booklet
  • they can be derived from chain rule
  • they are not essential to remember
  • they are not commonly used

What are exponential and logarithmic functions?

What are the derivatives of exponential functions?

These are also given in the formula booklet

How do I show or prove the derivatives of exponential and logarithmic functions?

What do the derivatives of exponentials and logarithms look like with a linear functions of x?