Essential Derivative Rules
Power Rule: d/dx(xⁿ) = nxⁿ⁻¹
Product Rule: (uv)' = u'v + uv'
Chain Rule: d/dx f(g(x)) = f'(g(x))·g'(x)
Product Rule: (uv)' = u'v + uv'
Chain Rule: d/dx f(g(x)) = f'(g(x))·g'(x)
Common Mistakes
- Forgetting the chain rule's inside derivative — differentiating (3x+1)² as 2(3x+1) instead of 6(3x+1) is one of the most common calculus errors.
- Using the power rule on products instead of the product rule for expressions like x²·sin(x).
Frequently Asked Questions
How do I know when to use the chain rule?
Whenever one function sits inside another, like sin(x²) or (3x+1)⁵ — anytime you see a function of a function, the chain rule applies.
What's the quotient rule for derivatives?
For u/v, the derivative is (u'v − uv') / v² — remember the order matters here, unlike the product rule which is symmetric.
