DERIVADAS*: Derivadas de funciones simples

${d \over dx} c = 0$

${d \over dx} x = 1$

${d \over dx} (cx) = c$

${d \over dx} x^c = cx^{c-1} \qquad \mbox{donde } x^c \mbox{ y } cx^{c-1} \mbox { se encuentran definidos}$

${d \over dx} (cx^n) = cnx^{n-1}$

${d \over dx} |x| = {x \over |x|} = \sgn x,\qquad x \ne 0$

${d \over dx} \left({1 \over x}\right) = {d \over dx} \left(x^{-1}\right) = -x^{-2} = -{1 \over x^2}$

${d \over dx} \left({1 \over x^c}\right) = {d \over dx} \left(x^{-c}\right) = -cx^{-c-1} = -{c \over x^{c+1}}$

${d \over dx}(\sqrt[n]{x}) = { 1 \over n \sqrt[n]{x^{n-1}} }\, \mbox{sea }x > 0$

${d \over dx} \sqrt{x} = {d \over dx} x^{1\over 2} = {1 \over 2} x^{-{1\over 2}} = {1 \over 2 \sqrt{x}}, \qquad x > 0$

${d \over dx} f(x)^n\ = nf(x)^{n-1} \cdot {d \over dx}f(x)$

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DERIVADAS*