Differentiation of sin x: d/dx (sin kx) = k cos kx
The differentiation of sin x is d/dx (sin kx) = k cos kx and d/dx (cos kx) = −k sin kx (x in radians).
What each letter means
- \(x\) the angle, in radians
- \(k\) a constant
When to use it
To find gradients, rates of change and stationary points of trig functions. With the chain rule, d/dx (sin kx) = k cos kx.
Worked example
Differentiate \(y=\sin^2x\).
- Chain rule: \(\dfrac{dy}{dx}=2\sin x\cos x\)
Answer: \(\dfrac{dy}{dx}=2\sin x\cos x=\sin2x\)
Common mistake
Losing the minus sign: the derivative of cos x is −sin x. And the results only hold with x in radians.
On your course
| Course | In the exam |
|---|---|
| Edexcel A Level (9MA0) | Not in the Edexcel booklet: learn it |
| Edexcel International A Level | Not in the booklet: learn it |
| AQA or OCR A Level | Check your board’s formula booklet: AQA formulae booklet (PDF) · OCR A Level Maths assessment page |
From our own A Level Maths formula sheets, in our words. Official: Pearson's formulae booklet (PDF) · Pearson's IAL formulae booklet (PDF).
Practise and revise
- Practise A Level Maths practice
- Revise Differentiation
- Revise IAL P3 further differentiation
- Print Edexcel A Level (9MA0) one-page formula sheet
Questions
What is the differentiation of sin x formula?
The differentiation of sin x is d/dx (sin kx) = k cos kx and d/dx (cos kx) = −k sin kx (x in radians). x: the angle, in radians; k: a constant.
Is the derivative of sin x given in the exam?
Edexcel A Level (9MA0): not in the Edexcel booklet: learn it. Edexcel International A Level: not in the booklet: learn it. AQA or OCR A Level: check your board’s formula booklet. This comes from our own A Level Maths formula sheets; your teacher has the official booklet.
Why must x be in radians?
The result comes from sin h / h → 1 as h → 0, which is only true when h is measured in radians.
Our own wording, examples and card, checked by A Level Math Revision. Not produced or endorsed by Pearson Edexcel, AQA or OCR.