Worked example 1
Differentiate a trig function
Differentiate y = 3 sin(2x) − 4 cos x
- Differentiate sin(2x) as 2 cos(2x)
- Multiply by the outside coefficient 3.
- Differentiate −4 cos x as +4 sin x.
Answer: dy/dx = 6 cos(2x) + 4 sin x
Higher Mathematics
Higher Maths Trigonometric differentiation
Practise trigonometric differentiation for Scottish Higher Mathematics with worked examples, clear methods and original interactive questions. Differentiate sin(kx) and cos(kx), including the sign and inner multiplier.
Before you start
- Differentiate powers.
- Work in radians for calculus.
- Apply the chain rule multiplier.
Explanation
The basic derivatives are d/dx(sin x) = cos x and d/dx(cos x) = −sin x. A multiplier inside the angle also appears outside by the chain rule.
These rules support tangents, stationary points and rates involving periodic models.
Method and rules
- d/dx(sin(kx)) = k cos(kx)
- d/dx(cos(kx)) = −k sin(kx)
- Angles are in radians for trigonometric calculus.
Worked examples
Worked example 2
Method check
Differentiate cos(5x)
- Include both the negative sign and inner multiplier.
So: -5 sin(5x)
Watch out
- Forgetting the negative derivative of cosine.
- Missing the multiplier inside kx.
- Using degree-mode reasoning in calculus.
Exam reminder
For trigonometric differentiation, show the defining equation or formula before simplifying. Check that every final value satisfies the original restrictions, interval or context.
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