d/dx (sinh^-1 x)
1 / √(x^2 + 1)
We can approach this problem by using the chain rule of differentiation. Let y = sinh^-1 x, then x = sinh y.
Differentiating both sides with respect to x, we get:
1 = cosh y * dy/dx
Solving for dy/dx , we get:
dy/dx = 1/cosh y
But, we know that cosh y = sqrt(x^2 + 1)
Therefore, dy/dx = 1/sqrt(x^2 + 1)
Thus, d/dx (sinh^-1 x) = 1/sqrt(x^2 + 1)
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