The idea of a function is that when you give it an input number, it will always give you a unique output number.
Examples:
y = 2x (y is a function of x)
h = 1/x2 + 5 (h is a function of x)
z = 23 + 3y - x + x/y (z is a function of x and y)
An equation simply tells you that two things are equal (left side is equal to the right side).
Examples:
y = 2x (note: also a function)
2x2 + 5 = 50 (not a function, but can be manipulated to become one: [x = squareroot of (50 - 5)/2])
2 + 19 = 21 (not a function)
All functions are equations, but not all equations are functions. Any equation where you have 1 input but more than 1 output is a relation. A function can have different inputs that give the same output, but not 1 input and multiple outputs (example: If you put 5 and -5 as inputs into the function y = x2, you will get the same output of 25.)
Differentiation: when you differentiate a function, you find a new function (the derivative) which expresses the old function's rate of change. For example, if f(x) = 2x, then the derivative f ' (x) = 2 for all x, because the function is always increasing by 2 units for every increase of x by 1 unit.A differential equation is an equation expressing a relationship between a named function and its derivatives. This can be as simple as y = y', where y is the original function and y' the derivative.
a quadratic equation must be in this form ax^2+bx+c=0 (can either be + or -) an exponential just means that the function grows at an exponential rate f(x)=x^2 or x^3
you simply differentiate the function and integrate the reamaing trigonometric equation leavin surd form in you ranswer
To differentiate Poisson's equation, which is given by (\nabla^2 \phi = -\frac{\rho}{\epsilon_0}), you apply the Laplacian operator (\nabla^2) to the potential function (\phi). This involves taking the second partial derivatives of (\phi) with respect to spatial variables. If you need to differentiate it with respect to time or other variables, you would need to consider the context of the problem, as Poisson's equation typically deals with static fields. Note that Poisson's equation itself is primarily a spatial differential equation.
The y-intercept is the value of the function (if it exists) when x = 0.
daffirentiate structure and function
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Differentiation: when you differentiate a function, you find a new function (the derivative) which expresses the old function's rate of change. For example, if f(x) = 2x, then the derivative f ' (x) = 2 for all x, because the function is always increasing by 2 units for every increase of x by 1 unit.A differential equation is an equation expressing a relationship between a named function and its derivatives. This can be as simple as y = y', where y is the original function and y' the derivative.
a quadratic equation must be in this form ax^2+bx+c=0 (can either be + or -) an exponential just means that the function grows at an exponential rate f(x)=x^2 or x^3
A function is a special type of relation. So first let's see what a relation is. A relation is a diagram, equation, or list that defines a specific relationship between groups of elements. Now a function is a relation whose every input corresponds with a single output.
you simply differentiate the function and integrate the reamaing trigonometric equation leavin surd form in you ranswer
ewan ko
You have to differentiate the equation. The dy/dx is the slope.
algebra
The y-intercept is the value of the function (if it exists) when x = 0.
dunctions are not set equal to a value
You can tell if an equation is a function if for any x value that you put into the function, you get only one y value. The equation you asked about is the equation of a line. It is a function.