Mathematics·Derivative·grades 10–11

Find the derivative of the function f(x) = sin(2x)

Problem

The function f(x) = sin(2x) is given. Find its derivative f′(x).

Answer

f′(x) = 2·cos(2x)

Step-by-step solution

Step 1. Spot the composite function
Inside the sine there is not just $x$ but $2x$ — a function inside a function. The chain rule applies: $(f(g(x)))' = f'(g)\cdot g'(x)$ .
Step 2. Derivative of the outer function
The derivative of sine is cosine: $(\sin u)' = \cos u$ . For now we leave the argument as it is: $\cos(2x)$ .

2 more steps — unlocked after you sign in:

Step 3. Multiply by the derivative of the inner function
Step 4. Answer

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Common mistakes

Writing just $\cos(2x)$ and forgetting to multiply by the derivative of the inner function (by 2).
Confusing the sign: the derivative of sine is plus cosine, and the minus appears with cosine.

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