Question
Find $\frac{d y}{d x}$ in the following:$$y=\sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right)$$
Step 1
The function is $\frac{2x}{1+x^{2}}$. Using the quotient rule, we get: $$ \frac{d}{dx}\left(\frac{2x}{1+x^{2}}\right) = \frac{2(1+x^{2}) - 2x(2x)}{(1+x^{2})^{2}} = \frac{2-2x^{2}}{(1+x^{2})^{2}} $$ Show more…
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