Derivatives and Derivative Theorems

The derivative from first principles, then the power, product, quotient and chain rules, implicit differentiation and higher derivatives.

10 questions, free, marked as you go with a worked explanation on every one.

What this covers

Use the definition of the derivative to find f′(3) for f(x) = x².
Given f(x) = 3x⁴ - 5x² + 7, find f′(2).
Given f(x) = (2x + 1)(x² - 3), use the product rule to find f′(1).
Given f(x) = (3x² + 1)⁵, use the chain rule to find f′(1).
Given f(x) = (x² + 1) / (x - 2), use the quotient rule to find f′(3).
Given f(x) = sin x, find the exact value of f′(π/3).
A circle is described by x² + y² = 25. Use implicit differentiation to find the slope of the tangent to the circle at the point (3, 4).
Given f(x) = x⁵ - 4x³, find the second derivative f″(1).
What is the derivative of f(x) = 5x³ - 2x?
Given f(x) = x³ - 6x, find f′(2).