LEARN · EXPLAIN · REVISE

Find f′(0), using radians.

Read the idea, work independently, then explain what changed.

TOPIC 01

Derivatives and their applications: mixed review

A mixed assessment: identify the method, justify it and revise your reasoning.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Transfer#Your turn

f(x)=\sin(33x)+\cos x

Quotient denominators stay nonzero; logarithms have positive real arguments and trigonometric derivatives use radians.

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Differentiate the specified function and substitute only after differentiating.

Hint 2

Use this intermediate relation.

f\prime(x)=t\cos(tx)-\sin x

Worked solution

The requested value is 33.

Checks and common pitfalls: A radian argument is essential for the familiar sine derivative formula.

Think first. Reveal a hint when the class is ready.

Teacher preparation and assessment