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A table of the first derivatives of common functions and used in calculus is presented.
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f(x)
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d [f(x)] / dx
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x n
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n x n - 1
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e x
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e x
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ln (x)
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1 / x
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sin x
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cos x
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cos x
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- sin x
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tan x
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sec 2x
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cot x
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- csc 2x
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sec x
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sec x tan x
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csc x
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- csc x cot x
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arcsin x
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1 / sqrt (1 - x 2)
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arccos x
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- 1 / sqrt (1 - x 2)
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arctan x
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1 / (1 + x 2)
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sinh x
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cosh x
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cosh x
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sinh x
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tanh x
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sech 2 x
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coth x
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- csch 2 x
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sech x
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- sech x tanh x
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csch x
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- csch x coth x
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arcsinh x
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1 / sqrt [x 2 + 1 ]
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arccosh x
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1 / sqrt [x 2 - 1 ]
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arctanh x
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1 / [ 1 - x 2 ]
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More on differentiation and derivatives
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