Beginner

Differentiation Basics

The rate at which one quantity changes with another.

STEP 1 · CONCEPT
The derivative is the slope of a curve at a point — instant rate of change.
STEP 2 · RULES
Power, product, quotient and chain rules cover most cases.
STEP 3 · ENGINEERING USE
Velocity is the derivative of displacement; current is the derivative of charge.
WORKED EXAMPLE
If x(t) = 5t², velocity v = dx/dt = 10t. At t = 3 s, v = 30 m/s.

Formulas

Power rule

d/dx (xⁿ) = n xⁿ⁻¹

Chain rule

dy/dx = dy/du · du/dx

Common

d/dx sin x = cos x ; d/dx eˣ = eˣ

Q1.d/dx (x³) = ?

Differentiation Basics · Easy

Q2.d/dx (sin 2x) = ?

Differentiation Basics · Medium

Q3.Derivative of a constant is…

Differentiation Basics · Easy