LEARN · EXPLAIN · REVISE

Find f′(0).

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 / Standard#Your turn

f(x)=e^{30x}

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)=te^{tx}

Worked solution

The requested value is 30.

Checks and common pitfalls: The natural exponential reproduces itself under differentiation.

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

Teacher preparation and assessment