A series of differentiation problems covering the main rules. Work through each one using the correct technique.
Formula Sheet
d/dx(xⁿ) = nxⁿ⁻¹chain: f′(g)·g′product: u′v + uv′d/dx(eˣ) = eˣd/dx(sin x) = cos xDifferentiate f(x) = 3x⁴ − 2x² + 5. What is f′(x) at x = 1?
Using the chain rule, differentiate y = sin(3x²). What is dy/dx?
Using the product rule, differentiate y = x²·eˣ. What is dy/dx at x = 0?
Which rule is used to differentiate y = √(4x + 1)?