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Derivative and Differentiation
The process of acquiring the derivative of a function or slope or gradient is referred to as differentiation or derivation. The derivative is denoted by (dy)/(dx) or f (x) and is provided by dividing the change in y variable by the change in x variable.
The derivative or slope or gradient of a line AB connecting points (x,y) and (x+dx, y + dy) is specified by
(Δy)/(Δx) = (change in y)/(change in x)
= (((y + (dy)) - y)/ (((x + (dx)) - x)
Whereas dy is a small change in y and dx is a small change in x variables.
2/4t=1/2
Metallic spheres of radii 6 centimetre, 8 centimetre and 10 centimetres respectively are melted to form a single solid sphere. Find the radius of the resulting sphere.
Definition Assume that f(t) is a piecewise continuous function. The Laplace transform of f(t) is denoted L{ f (t )} and defined by, There is an optional notation for L
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