# Chapter Two - Differentials

prior knowledge

Derivatives

The y
with respect to x
is
written as \frac[[dy]][[dx]]
.

Thef(x)
can also be written as f'(x)

You already know these rules:c
is a constant, then

**derivative**ofThe

**derivative function**ofYou already know these rules:

**Sum rule**:y = f(x)+g(x) \implies \frac[[dy]][[dx]] = f'(x)+g'(x) **Power rule**:y = x^n \implies \frac[[dy]][[dx]] = n \cdot x^[[n-1]]

y = c \implies \frac[[dy]][[dx]] = 0 y = c\cdot f(x) \implies \frac[[dy]][[dx]] = c\cdot f'(x)

## Exercise 1

Try to find the following derivatives.

a

b

practice

theory

Tangent

A tangent is an equation of a straight line that defines the slope of a graph in a specific point. The tangent of a function
f(x)
for point p
is defined by the function
that goes through point p
and as slope the gradient of the function f(x)
at point p
.
Remember: the gradient of a function in a specific point, is the value for that point of the derivative of the function.