CPM Homework Help : CALC Problem 7-187

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7-187.

For each of the following functions, find $\frac { d y } { d x }$ .

$y =\operatorname{sin}^{−1}( \sqrt { 1 - x } )$
Hint (a):
Be mindful about positive and negative values.

$y=\frac { 2 \operatorname { cos } x } { \sqrt { 1 + x ^ { 2 } } }$
Hint (b):
Quotient Rule.

$y = xe^{\operatorname{sec} x}$
Hint (c):
Chain Rule.
$\text{Recall that }\frac{d}{dx}\text{ sec}x=\text{sec}x\text{tan}x$

$\operatorname{ln} y = x \operatorname{ln} x$
Hint (d):
Implicit differentiation.

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