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Differentiation Rules

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 travelling. 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 a derivative is called differentiation. The fundamental theorem of calculus states that differentiation is the reverse process to integration. - Wikipedia

Product Rule
If f (x) and g (x) are differentiable, then

[ f (x) g (x) ] ' = f (x) g ' (x) + g (x) f ' (x)

 

Quotient Rule

If f (x) and g (x) are differentiable and g (x) ¹ 0, then
Power Rule

If f (x) = xn, where n is a positive integer, then
f ' (x) = n xn-1
Chain Rule

If y = f (u) and u = g (x)
and both are differentiable, then

 


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