Differentiable

Definition of Differentiable Differentiable means:  the function has derivative the derivative f’(x) must exist for every value in the function’s domain Examples The use of differentiable function When a function is differentiable, we can use all the power of calculus when working with it. When a function is differentiable, it is continuous. Differentiable ⇒ Continuous … Continue reading "Differentiable"

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Integration by Substitution (Reverse Chain Rule)

Definition Integration by Substitution (also called “The Reverse Chain Rule” or “u-Substitution” ) is a method to find an integral, but only when it can be set up in a special way. Examples f(x) dx u du Substitution Integral of ∫ f(u) du Integral of ∫ f(x) dx ∫ (x+1)3 dx x+1 1 dx ∫ u3 du ∫ … Continue reading "Integration by Substitution (Reverse Chain Rule)"

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Calculus

Calculus is the mathematical study of continuous change. The 2 branches are related to each other by the fundamental theorem of calculus. Both branches make use of the fundamental notions of convergence of infinite series & infinite sequences to a well-defined limit. Derivatives (Differential) Differentiable Common Derivatives Implicit Differentiation Homogeneous Differential Equations Integration (Integral) Integration … Continue reading "Calculus"

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