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derivative : In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much a quantity is changing at a given point. For example, the derivative of the position (or distance) of a vehicle with respect to time is the instantaneous velocity (respectively, instantaneous speed) at which the vehicle is traveling. Conversely, the integral of the velocity over time is the vehicle's position. The derivative of a function at a chosen input value describes the best linear approximation of the function near that input value. For a real-valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the graph of the function at that point. In higher dimensions, the derivative of a function at a point is a linear transformation called the linearization. A closely related notion is the differential of a function. The process of finding.... More from Wikipedia
derivative : In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much a quantity is changing at a given point. For example, the derivative of the position (or distance) of a vehicle with respect.. More from Wikipedia
Derivation
The figure shows an object AB at a distance u from the pole of a concave mirror. The image A 1 B 1 is formed at a distance v from the mirror. The position of the image is obtained by drawing a ray diagram. Consider the D A 1 CB 1 and D ACB [when two angles of D A 1 CB 1 and D ACB are equal then the..
The figure shows an object AB at a distance u from the pole of a concave mirror. The image A 1 B 1 is formed at a distance v from the mirror. The position of the image is obtained by drawing a ray diagram. Consider the D A 1 CB 1 and D ACB [when two angles of D A 1 CB 1 and D ACB are equal then the..Derivative of a Function
Derivative of a Function - So far we have discussed the derivative of a function f(x) at a point 'a' which is in the domain of f. Suppose we want to find the derivative of the same function at a different point 'b', then we have to compute the derivative by r..
MORE AT www.mathtv.com Part 0: The definition of a derivative
Finding the slope of a tangent line to a curve (the derivative). Introduction to Calculus.
Question : I am currently doing AS level maths and I am not entirely sure when one has to use the integration method or diferentiation? What are the indicators in a questions whether to implement integration or find the derivative?
Answer : If you have a function and the question asks for a rate, the correct operation is differentiation; if you have a function, and it is already a rate, or derivative, to find the function that it came from you need to integrate; for example, suppose they tell you that an object has a velocity given by v = 3x + 5 Question: Where is the object at any time? ans Int(3x + 5) = (3/2)x^2 + 5x + C (the constant will be found if you're given the time interval of motion) Question: What is the acceleration of the object? v' = d(3x + 5)/dx = 3, because acceleration is the rate of change of velocity. Good luck.. More from Yahoo Answers
Answer : If you have a function and the question asks for a rate, the correct operation is differentiation; if you have a function, and it is already a rate, or derivative, to find the function that it came from you need to integrate; for example, suppose they tell you that an object has a velocity given by v = 3x + 5 Question: Where is the object at any time? ans Int(3x + 5) = (3/2)x^2 + 5x + C (the constant will be found if you're given the time interval of motion) Question: What is the acceleration of the object? v' = d(3x + 5)/dx = 3, because acceleration is the rate of change of velocity. Good luck.. More from Yahoo Answers
Question : What do you do when you need to find the derivative of a certain curve, but the function is unkown, or the curve isn't represented by a function? What if, for example, you have a graph of the changing speed of a car, where the speed is not determined by a function, but rather simply by the alteration of the pedal by the driver? What I mean to say is that a graph exists, but it is kind of abstract. The graph only shows what happens - it's an experimental thing - not what is known to happen with..
Answer : Those graphs are usually a collection of connected line segments. These line segments each have a slope, which can be found by m = ((y2 - y1)/(x2 - x1)) using the endpoints of the segment. The slope at a point = the derivative at that point. Velocity is the first derivative of Position Acceleration is the first derivative of Velocity and so the second derivative of Position. And as a bonus, the "Jerk" is the derivative of Acceleration. It's when you feel yourself jerked back into the seat when the car you're in accelerates or you lean forward when it brakes... More from Yahoo Answers
Answer : Those graphs are usually a collection of connected line segments. These line segments each have a slope, which can be found by m = ((y2 - y1)/(x2 - x1)) using the endpoints of the segment. The slope at a point = the derivative at that point. Velocity is the first derivative of Position Acceleration is the first derivative of Velocity and so the second derivative of Position. And as a bonus, the "Jerk" is the derivative of Acceleration. It's when you feel yourself jerked back into the seat when the car you're in accelerates or you lean forward when it brakes... More from Yahoo Answers