7. Given that \(y = \arcsin x , - 1 \leq x < 1\),
- show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 1 } { \sqrt { 1 - x ^ { 2 } } }\).
Given that \(f ( x ) = \frac { 3 x + 2 } { \sqrt { 4 - x ^ { 2 } } }\),
- show that the mean value of \(f ( x )\) over the interval \([ 0 , \sqrt { } 2 ]\), is
$$\frac { \pi \sqrt { } 2 } { 4 } + A \sqrt { } 2 - A$$
where \(A\) is a constant to be determined.
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