Derivatives
Differentiation rules, the chain rule, inverse functions and what derivatives tell you about a graph.
Problems
- Differentiability of a Piecewise Function
- Linear Piece Matched to a Power Function
- A Quartic Divided by x² − 1
- Ratios of One-Sided Derivatives
- Derivative of a Self-Composition
- Inverse Derivative of x³ + 3x
- Chain Rule with Differential Equation
- Derivatives of an Inverse Function
- Derivative of an Intersection Point
- An Increasing Function Meets Its Inverse
- The Chain Rule Through an Inverse
- A Cubic Composed with eˣ
- A Cubic Whose Inverse Is Flat
- A Bell Curve Minus a Line
- Slope of a Parametric Curve
- Local Extremes of an Integral Function
- Shortest Distance to ln x
- A Parametric Slope at Infinity
- Closest Point on a Semicubical Parabola
- Largest Triangle with a Point on √(3x)
- Maximum times Minimum of x e^(−x²)
- A Parametric Second Derivative
- Parametric Sums at t = 0
- A Parametric Second Derivative II
- The Largest Inscribed Trapezoid
- When an Integral Function Has One Extremum
- A Limit as a Derivative
- A Polynomial Defined by Its Own Derivative
- Derivative of a Ratio of Geometric Sums
- A Quotient Derivative at √π
- A Derivative from the Definition
- A Multiplicative Function's Derivative
- Functional Equation with two variables I
- Cubic Polynomial Limit
- Polynomial Limit I
- An Exponential Tangent to a Line
- Logarithmic Derivative of an Even Function
- Derivative Ratio of a Product Polynomial
- Constants from a Limit at x = 1
- Counting Real Roots
- The 8th Derivative at Zero
- A Functional Equation for a Polynomial
- A Logarithmic Derivative of a Long Product
- A Triangle Under a Logarithm
- A Tenth Derivative
- Functional Equation with two variables II
- A Polynomial from a Differential Identity
- A Functional Equation for f′
- A Derivative Known Only Up to Sign
- A Shifted Polynomial Glued Together
- Two Curves Meeting Twice
- Extrema of f(x) − x² from a Graph
- A Function Hidden in an Integral Equation
- Three Conditions Fixing a Function
- A Cubic Caught Between Two Bounds