Mathematics•Medium

Derivative Challenge

Mathematics challenge: Derivatives measure the instantaneous rate of change. Apply chain rule, product rule, and more.

Scenario

A series of differentiation problems covering the main rules. Work through each one using the correct technique.

Question 1

Differentiate f(x) = 3x⁴ − 2x² + 5. What is f′(x) at x = 1?

Question 2

Using the chain rule, differentiate y = sin(3x²). What is dy/dx?

cos(3x²)6x·cos(3x²)3x·cos(3x²)−6x·cos(3x²)

Question 3

Using the product rule, differentiate y = x²·eˣ. What is dy/dx at x = 0?

Question 4

Which rule is used to differentiate y = √(4x + 1)?

Product ruleQuotient ruleChain rulePower rule only

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