Differentiation of sin x: d/dx (sin x) = cos x
The differentiation of sin x is d/dx (sin x) = cos x and d/dx (cos x) = −sin x (x in radians).
What each letter means
- \(x\) the angle, in radians
- \(\frac{d}{dx}\) differentiate with respect to x
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
Find the gradient of \(y=3\sin x-2\cos x\) at \(x=\dfrac{\pi}{2}\).
- \(\dfrac{dy}{dx}=3\cos x+2\sin x\)
- At \(x=\tfrac\pi2\): \(3(0)+2(1)\)
Answer: gradient \(=2\)
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 |
|---|---|
| AA SL | In the IB formula booklet |
| AA HL | In the IB formula booklet |
| AI HL | In the IB formula booklet |
From our own IB Maths formula sheets, in our words. The IB gives its booklet to schools, so we checked against our own copy: your teacher has the official one. Official: IB DP Mathematics page.
Practise and revise
- Practise AA SL rules of differentiation questions
- Revise Differentiation (AA SL)
- Revise Differentiation (AA HL)
- Tool Graph of y = sin x
- Print AA SL one-page formula sheet
Questions
What is the differentiation of sin x formula?
The differentiation of sin x is d/dx (sin x) = cos x and d/dx (cos x) = −sin x (x in radians). x: the angle, in radians; d/dx: differentiate with respect to x.
Is the derivative of sin x given in the exam?
AA SL: in the IB formula booklet. AA HL: in the IB formula booklet. AI HL: in the IB formula booklet. This comes from our own IB 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 IB Math Revision. Not produced or endorsed by the International Baccalaureate Organization.