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transgalactic
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here is the question and how i tried to solve it??
http://img510.imageshack.us/img510/441/60031828xt4.th.gif
http://img510.imageshack.us/img510/441/60031828xt4.th.gif
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Differentiation proof is a mathematical process used to find the rate of change of a function. It involves finding the derivative of a function, which represents the slope of the tangent line at any given point on the function.
To prove differentiation, you must use the definition of the derivative, which states that the derivative of a function f(x) at a point x is equal to the limit as h approaches 0 of [f(x+h) - f(x)] / h. This limit will give you the slope of the tangent line at that point, also known as the derivative.
Differentiation is the process of finding the derivative of a function, while integration is the process of finding the antiderivative of a function. In other words, differentiation finds the rate of change of a function, while integration finds the original function from its derivative.
Differentiation has many real-life applications, including in physics, economics, and engineering. For example, it can be used to find the velocity and acceleration of an object at a given time, determine the optimal production level for a company, or calculate the slope of a curve in a circuit diagram.
Yes, there are several shortcut rules for differentiation, such as the power rule, product rule, quotient rule, and chain rule. These rules allow you to find the derivative of more complex functions without having to use the definition of the derivative every time. However, it is important to understand the definition and how these rules are derived in order to use them correctly.