Difference between r1.3 and the current
@@ -7,5 +7,10 @@
$=\frac{\cosh^2x-\sinh^2x}{\cosh^2x}$
$=\frac1{\cosh^2x}$
$=\operatorname{sech}^2 x$
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Up: [[여러가지증명]]
$=\frac1{\cosh^2x}$
$=\operatorname{sech}^2 x$
KWs:
hyperbolic tangent derivative proof
쌍곡탄젠트 미분 증명
Up: [[여러가지증명]]
증명 ¶
$\displaystyle (\tanh x)'=\left(\frac{\sinh x}{\cosh x}\right)'$
$\displaystyle =\frac{(\sinh x)'\cosh x-\sinh x(\cosh x)'}{\cosh^2 x}$
$\displaystyle =\frac{\cosh^2x-\sinh^2x}{\cosh^2x}$
$\displaystyle =\frac1{\cosh^2x}$
$\displaystyle =\operatorname{sech}^2 x$
KWs:$\displaystyle =\frac{\cosh^2x-\sinh^2x}{\cosh^2x}$
$\displaystyle =\frac1{\cosh^2x}$
$\displaystyle =\operatorname{sech}^2 x$
hyperbolic tangent derivative proof
쌍곡탄젠트 미분 증명
쌍곡탄젠트 미분 증명
Up: 여러가지증명