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Differentiating Special Functions (DP IB Maths: AI HL)
Revision Note
Differentiating Trig Functions
How do I differentiate sin, cos and tan?
- The derivative of is
- The derivative of is
- The derivative of is
- This result can be derived using quotient rule
- All three of these derivatives are given in the formula booklet
- For the linear function, where and are constants,
- the derivative of is
- the derivative of is
- the derivative of is
- For the general function,
- the derivative of is
- the derivative of is
- the derivative of is
- These last three results can be derived using the chain rule
- For calculus with trigonometric functions angles must be measured in radians
- Ensure you know how to change the angle mode on your GDC
Examiner Tip
- As soon as you see a question involving differentiation and trigonometry put your GDC into radians mode
Worked example
a)
Find for the functions
b) A curve has equation.
Find the gradient of the tangent to the curve at the point where .
Give your answer as an exact value.
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Differentiating e^x & lnx
How do I differentiate exponentials and logarithms?
- The derivative of is where
- The derivative of is where
- For the linear function , where and are constants,
- the derivative of is
- the derivative of is
- in the special case , ('s cancel)
- For the general function ,
- the derivative of is
- the derivative of is
- The last two sets of results can be derived using the chain rule
Examiner Tip
- Remember to avoid the common mistakes:
- the derivative of with respect to is, NOT
- the derivative of with respect to is , NOT
Worked example
A curve has the equation.
Find the gradient of the curve at the point where gving your answer in the form , where and are integers to be found.
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