Derivatives Flashcards
d/dx
An operation meaning to take the derivative with respect to X.
dy/dx
An operation meaning the derivative of y with respect to x
f (x)
A function in terms of X
Derivative
A new function we find that tells us the instantaneous rate of change at each point of the old function, or the slope of the tangent line to the curve of EVERY point of the original function.
Polynomials
An expression composed of variables and exponents, combined using the mathematical operations.
Power Rule
A rule helping find the derivative of a variable raised to the power, by taking the exponent and multiplying it by the coefficient, then decreasing exponent by 1.
Constant Rule
This states that derivative of a constant function is zero.
Product Rule
The derivative of a product of two functions is the first function times the derivative of the second function, plus the second function times the derivative of the first function.
Quotient Rule
The derivative of a quotient is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator.
Derivative Notation
The mathematical expression of a derivative ie; fâ(x) for f(x)
Leibnizs Notation
This utilises symbols dy and dy,, used in situations involving many changing quantities.
Newtons Notation
Most commonly used in physics where derivative of f is expressed as f with a dot above it and derivative of y = f(x) represented as a y with a dot above it
