Intuitive Calculus Blog

The First Derivative Test: Intuition and Examples

The first derivative test is one of those ideas that confuses almost every student learning calculus for the first time. Here we'll learn the intuitive idea behind this test...

Continue reading "The First Derivative Test: Intuition and Examples"

Critical Points of a Function: Intuition and Examples

Let's talk about critical points of a function. In this page I'll show you the intuition behind this concept and we'll go over a lot of examples on how to find them...

Continue reading "Critical Points of a Function: Intuition and Examples"

A Complete Guide to the Essential Calculus Problems

The Calculus Problems Manual contains the essential exercises you need to know how to solve to get an outstanding grade in a calculus course.

Continue reading "A Complete Guide to the Essential Calculus Problems"

Linear Approximations in Calculus: Intuition and Examples

The linear approximation of functions is one of the most important applications of the derivative. In this page we'll see the intuitive idea behind this and some examples...

Continue reading "Linear Approximations in Calculus: Intuition and Examples"

Solving Derivatives: All The Tricks and Techniques

In this page you'll find everything you need to know about solving derivatives. My goal with this page is to make you into a derivative solving machine :-)

Continue reading "Solving Derivatives: All The Tricks and Techniques"

The Derivative of The Inverse of a Function: Intuition and Examples

The rule for the derivative of the inverse of a function has always been a confusing point for students. In this page I explain this topic detail, so you can leave without any doubt about it...

Continue reading "The Derivative of The Inverse of a Function: Intuition and Examples"

The Derivative of an Integral: Intuition and Examples

What is the derivative of an integral? This question is asked by many readers, so I decided to write a special page to explain this topic in detail. It happens that the derivative is the inverse...

Continue reading "The Derivative of an Integral: Intuition and Examples"

The Derivative of tan(x)

The derivative of tan(x) is 1/cos^2(x). We'll prove this fact using a simple method, which involves only the product rule.

Continue reading "The Derivative of tan(x)"

Formulas for the Derivative of Inverse Trig Functions

In this page you'll find the formulas for the derivative of inverse trig functions. These formulas are quite useful and easy to forget. I'll also show you an easy method for deducing these formulas...

Continue reading "Formulas for the Derivative of Inverse Trig Functions"

Implicit Differentiation: Intuition and Examples

Implicit differentiation confuses many calculus students. That's not because it is hard. In fact, it is just an application of the chain rule. And that's the secret...

Continue reading "Implicit Differentiation: Intuition and Examples"

The Derivative of ln(x): Intuition, Proof and Examples

In this page we'll prove the formula for the derivative of ln(x), and we'll also give it some intuitive meaning. Then we'll solve tons of examples involving derivaitves of logarithms...

Continue reading "The Derivative of ln(x): Intuition, Proof and Examples"

New! Comments

Do you have a doubt, or want some help with a problem? Leave a comment in the box below.