Velocity, Acceleration and Displacement: Formulas and Graphs
Velocity, acceleration and displacement explained: average and instantaneous formulas, motion graphs, calculus links and worked examples.
Tag: derivatives
Read article → Velocity, Acceleration and Displacement: Formulas and Graphs
Limits and Derivatives (Class 11): Formulas and Solved Examples
Class 11 Limits and Derivatives: algebra of limits, standard and trig limits, derivatives from first principles and the rules, with solved examples.
Derivative Rules: Every Differentiation Formula, Explained
All the derivative rules in one place: definition, power, product (uv), quotient and chain rules, plus trig, exponential, log and inverse trig derivatives.
Derivative of sin x: Proof, Examples and Trig Derivatives
The derivative of sin x is cos x. See the limit proof, chain rule examples like sin(3x) and sin²x, and the table of all six trig derivatives.
Calculus 1 vs Calculus 2: What Each Course Covers
What Calc 1 and Calculus 2 cover topic by topic, which is harder, what comes next, and a study plan with free guides and step-by-step calculators.
Optimization Problems in Calculus: 4 Solved Examples
Solve calculus optimization problems in 6 steps. Worked examples: the largest fenced area, the open box, the cheapest can and the closest point on a curve.
Related Rates: Step-by-Step Strategy and Classic Problems
Solve related rates problems in 6 steps. Worked classics: the sliding ladder, the expanding balloon, the draining cone and the moving shadow.
Mean Value Theorem: Statement, Meaning and Worked Examples
The Mean Value Theorem guarantees a point where the instantaneous rate equals the average rate. Hypotheses, Rolle’s theorem, and how to find c step by step.
Linear Approximation (Linearization): Formula and Examples
Linear approximation uses the tangent line L(x) = f(a) + f'(a)(x − a) to estimate values like √4.1 and sin 0.1. Includes error, differentials and examples.
Newton’s Method: Formula, Worked Example and When It Fails
Newton’s method finds roots with xₙ₊₁ = xₙ − f(xₙ)/f'(xₙ). Step-by-step iterations for x³ − 2x − 5, approximating √2, and when the method fails.