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$Old$ October 26th, 2009, 07:40 AM

JessicaWade $JessicaWade is offline$

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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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$Old$ October 26th, 2009, 07:53 AM

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Originally Posted by JessicaWade $View Post$

Show the derivative of y = sinh^(-1)x = ln(x + squareroot(x^2+1) reduces to ((1)/(squareroot(x^2 + 1))

$\begin{aligned}y^{\prime}&=\frac{1}{x+\sqrt{x^2+1}}\cdot\left(1+x\left(x^2+1\right)^{-1/2}\right)\\ &=\frac{x+\sqrt{x^2+1}}{\sqrt{x^2+1}\left(x+\sqrt{x^2+1}\right)}\\ &=\frac{1}{\sqrt{x^2+1}}\end{aligned}$

Does this make sense?

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