Show the derivative of y = sinh^(-1)x = ln(x + squareroot(x^2+1) reduces to ((1)/(squareroot(x^2 + 1))
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Originally Posted by JessicaWade Show the derivative of y = sinh^(-1)x = ln(x + squareroot(x^2+1) reduces to ((1)/(squareroot(x^2 + 1)) $\displaystyle \begin{aligned}y^{\prime}&=\frac{1}{x+\sqrt{x^2+1} }\cdot\left(1+x\left(x^2+1\right)^{-1/2}\right)\\ &=\frac{x+\sqrt{x^2+1}}{\sqrt{x^2+1}\left(x+\sqrt{ x^2+1}\right)}\\ &=\frac{1}{\sqrt{x^2+1}}\end{aligned}$ Does this make sense?
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