| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chain Rule |
| Type | Differentiation of trigonometric composites |
| Difficulty | Moderate -0.5 This is a straightforward application of the quotient rule to tan x = sin x / cos x, requiring only direct substitution of known derivatives and basic trigonometric identities. It's slightly easier than average because it's a standard proof with a clear method and no problem-solving required, though it does require careful algebraic manipulation. |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.07q Product and quotient rules: differentiation |
Use the derivatives of $\sin x$ and $\cos x$ to prove that the derivative of $\tan x$ is $\sec^2 x$. [4]
\hfill \mbox{\textit{Edexcel C3 Q1 [4]}}