Table of Contents
- 1 What does the derivative of y with respect to X mean?
- 2 How do you find the derivative of y with respect to x?
- 3 What is integral of x with respect to x?
- 4 Can we integrate y with respect to x?
- 5 What is the integration of X with respect to X?
- 6 How do you calculate derivative?
- 7 Does this relation define y as a function of X?
What does the derivative of y with respect to X mean?
The derivative of a function y = f(x) of a variable x is a measure of the rate at which the value y of the function changes with respect to the change of the variable x. It is called the derivative of f with respect to x.
How do you find the derivative of y with respect to x?
Given y = f(x) g(x); dy/dx = f’g + g’f. Read this as follows: the derivative of y with respect to x is the derivative of the f term multiplied by the g term, plus the derivative of the g term multiplied by the f term.
What does it mean by with respect to X?
Say we consider y=f(x). The terminology “with respect to x” just means that x is the variable that we are changing, and we want to see how y reacts to the small little changes in x.
What is the integration of y with respect to x?
If the example had not given an integration range, the answer would be x3 + x + c. If you are calculating the indefinite integral of y with respect to x (i.e., if the range of integration is not defined), you need to add an arbitrary constant “+ c” to the end of the equation.
What is integral of x with respect to x?
with respect to x it is x^2/2. but for some other variable say t it is xt. Integration is an important tool in calculus that can give an antiderivative or represent area under a curve. The indefinite integral of f(x), denoted int f(x)\ dx, is defined to be the antiderivative of f(x).
Can we integrate y with respect to x?
To answer your question: “So what does one do about the integral of y with respect to x? ” one does NOTHING. y is an unknown function of x so we can’t integrate.
What does with respect to Y mean?
The derivative with respect to x is: “at what rate does f change as x changes”, in this case it is a constant, 1. At what rate does f change as y changes, i.e. “the derivative with respect to y”, which goes like 2y.
What is integral of a X with respect to X?
By differentiating you can recognise the integral will be (a^x)/ln(a) +c or you can perform a u substitution where u=a^x then du=ln(a)a^xdx. dx=1/ln(a) * 1/u * du. Therefore the integral is now u/(u*ln(a)) du = 1/ln(a) du = u/ln(a) +c = a^x/ln(a) +c.
What is the integration of X with respect to X?
Integration Rules
Common Functions | Function | Integral |
---|---|---|
Variable | ∫x dx | x2/2 + C |
Square | ∫x2 dx | x3/3 + C |
Reciprocal | ∫(1/x) dx | ln|x| + C |
Exponential | ∫ex dx | ex + C |
How do you calculate derivative?
The first step to finding the derivative is to take any exponent in the function and bring it down, multiplying it times the coefficient. We bring the 2 down from the top and multiply it by the 2 in front of the x. Then, we reduce the exponent by 1. The final derivative of that term is 2*(2)x1, or 4x.
How to calculate derivative?
Formula for calculating the derivative of a function sum : (u+v)’ = u’+v’
What is the formula for derivatives?
Power Rule: (d/dx) (xn ) = nxn-1
Does this relation define y as a function of X?
A function is a relation in which each input has only one output. In the relation , y is a function of x, because for each input x (1, 2, 3, or 0), there is only one output y.