About: Proofs of common derivative shortcuts   Sponge Permalink

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The derivative of a function f(x) (noted as f'(x)) is defined as: An alternate definition is: However, because of how tedious it is to use the definition of a derivative every time the derivative of a function is needed, there are shortcuts known as differentiation formulas which reduce the amount of work needed to differentiate functions. Here, we will prove that these shortcuts work.

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  • Proofs of common derivative shortcuts
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  • The derivative of a function f(x) (noted as f'(x)) is defined as: An alternate definition is: However, because of how tedious it is to use the definition of a derivative every time the derivative of a function is needed, there are shortcuts known as differentiation formulas which reduce the amount of work needed to differentiate functions. Here, we will prove that these shortcuts work.
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  • The derivative of a function f(x) (noted as f'(x)) is defined as: An alternate definition is: However, because of how tedious it is to use the definition of a derivative every time the derivative of a function is needed, there are shortcuts known as differentiation formulas which reduce the amount of work needed to differentiate functions. Here, we will prove that these shortcuts work.
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