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Derivadas de funciones hiperbólicas

De por WikiMatematica.org


Contenido

sinh(x)

\frac{\mathrm{d} }{\mathrm{d} x} (\sinh (x))= \cosh (x) 


cosh(x)

\frac{\mathrm{d} }{\mathrm{d} x} (\cosh(x))= \sinh (x) 


tanh(x)

\frac{\mathrm{d} }{\mathrm{d} x} (\tanh (x))= sech^{2} (x) 


csch(x)

\frac{\mathrm{d} }{\mathrm{d} x} (csch (x))= -csch(x) \coth (x) 


sech(x)

\frac{\mathrm{d} }{\mathrm{d} x} (sech (x))= -sech(x) \tanh (x) 


coth(x)

\frac{\mathrm{d} }{\mathrm{d} x} (\coth (x))= -csch(x) 


--Jorgetr 22:09 3 ago 2009 (CST)

funciones hiperbólicas Inversas


sinh^{-1}(x)

\frac{\mathrm{d} }{\mathrm{d} x} (\sinh^{-1}(x))= \frac{1}{\sqrt{1+x^{2}}} 



cosh^{-1}(x)

\frac{\mathrm{d} }{\mathrm{d} x} (\cosh^{-1}(x))= \frac{1}{\sqrt{x^{2}-1}} 



tanh^{-1}(x)

\frac{\mathrm{d} }{\mathrm{d} x} (\tanh^{-1}(x))= \frac{1}{1-x^{2}} 


csch^{-1}(x)

\frac{\mathrm{d} }{\mathrm{d} x} (csch^{-1} (x))= \frac{1}{ \left | x \right |\sqrt{x^{2}+1}}


sech^{-1}(x)

\frac{\mathrm{d} }{\mathrm{d} x} (sech^{-1} (x))= \frac{1}{  x \sqrt{1-x^{2}}}


coth^{-1}(x)

\frac{\mathrm{d} }{\mathrm{d} x} (\coth (x))=\frac{1}{1-x^{2}} 


--Jorgetr 19:19 9 ago 2009 (CST)

Ejemplo # 1

y=xcosh(x)

y'=xsenh(x)+cosh(x)

Ejemplo # 2

y=xsenh(x^2)

y'=2xcosh(x^2)

Ejemplo # 3

y=tanh(e^t)

y'=e^tsech^2(e^t)

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