Question

Find \frac{\mathrm{d} y}{\mathrm{d} x}, if y=xsin^{-1}\,x+\sqrt{1-x^{2}}.

11 Mar 2024
Answer :
Word Count : 262
We are tasked with finding the derivative of the function \( y = x \sin^{-1}(x) + \sqrt{1 - x^2} \) with respect to \( x \). Let's proceed with the calculation step by step. ### Step 1: Differentiate \( y = x \sin^{-1}(x) + \sqrt{1 - x^2} \) We will use the following derivative rules: 1. Product Rule: For two functions \( u(x) \) and __________ _______ __________ ______ ________ ______ ________ ____ ______ ___ _________.
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