arctanh_x_미분_증명 Copy: arctanh_x_미분_증명 has NO comma Hide Show [edit] Theorem ¶ $\displaystyle {d\over dx}(\tanh^{-1}x)=\frac1{1-x^2}$ [edit] Proof ¶ $\displaystyle y=\tanh^{-1}x$ $\displaystyle \tanh{y}=x$ $\displaystyle \frac{dy}{dx}=\frac1{\;\frac{dx}{dy}\;}$ $\displaystyle =\frac1{\operatorname{sech}^2 y}$ $\displaystyle =\frac1{1-\tanh^2 y}$ $\displaystyle =\frac1{1-x^2}$ Up: 여러가지증명
