Chapter Two - Differentials
prior knowledge
Derivatives
The derivative of y
with respect to x
is
written as \frac[[dy]][[dx]]
.
The derivative function off(x)
can also be written as f'(x)
You already know these rules:c
is a constant, then
The derivative function of
You 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.
