Let \(f(x) = x^2\). Evaluate \(f'(3)\) using first principles.

Let \(f(x) = x^2 + 3x - 1\). Evaluate \(f'(2)\) using first principles.

Let \(f(x) = x^3\). Evaluate \(f'(2)\) using first principles.

Limit Definition of Derivative Square Root, Fractions, 1/sqrt(x), Examples - Calculus

The Organic Chemistry Tutor

Let \(f(x) = \sqrt{x + 2}\). Evaluate \(f'(7)\) using first principles.

Let \(f(x) = \dfrac{x + 2}{x - 2}\). Evaluate \(f'(6)\) using first principles.

Let \(f(x) = \dfrac{1}{\sqrt{x - 2}}\). Evaluate \(f'(3)\) using first principles.

Conclude by giving your students these challenges:

- Chances Are by NRICH
- Equal Equilateral Triangles by NRICH
- Areas of Parallelograms by NRICH
- Area in a Polygon

The three angles pictured below are equal. Mentally determine the fraction that's shaded.

Here's the answer.