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Level 455

Exponential Change, Separable Differential Equatio


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d/dx(arcsin)
=1/(√1-x2)
d/dx(arctan)
=1/(1+x2)
d/dx(arcsec)
=1/(|x|√x2-1)
∫(du/(√a2-x2))
=arcsin(u/a)+C
∫(du/(√a2+x2))
=(1/a)*arctan(u/a)+C
∫(du/(x(√x2-a2)))
=(1/a)*arcsec|u/a|+C
sinh(x)
=(ex-e-x)/2
cosh(x)
=(ex+e-x)/2
cosh2x-sinh2x
=1
sinh(2x)
=2sinh*cosh
cosh(2x)
=cosh2x+sinh2x
cosh2x
=(cosh(2x)+1)/2
sinh2x
=(cosh(2x)-1)/2
tanh2x
=(1-sech2x)
d/dx(sinh)
=cosh
d/dx(cosh)
=sinh
d/dx(tanh)
=sech^2
d/dx(sech)
=-sech*tanh
∫sinh
=cosh+C
∫cosh
=sinh+C
∫sech2
=tanh+C
∫sech*tanh
=-sech+C