Chapter Two - Differentials

 prior knowledge
The derivative of y with respect to x is written as \frac[[dy]][[dx]] .
The derivative function of f(x) can also be written as f'(x)

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]]
If c is a constant, then
  • 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 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.

Exercise 2

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