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Implicit Differentiation

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Please help & please show step-by-step, thx, appreciate it.
Below are notes my instructor gave for this assignment that are relative and important. The problems are below. There is 1 problem at the bottom of the page. Thank you.

When differentiating keep in mind the variable with respect you differentiate. For example, the Chain Rule gives us , or . Implicit differentiation
Implicit differentiation is a technique based on the Chain Rule that allows us to differentiate equations involving both independent and dependent variables. For example, we can find the derivative of the function defined by the equation without first solving for .

. The last equation can be solved for . margin{ When differentiating keep in mind the variable with respect you differentiate. For example, the Chain Rule gives us , or . }

Derivatives of inverse trigonometric functions
By differentiating the equation we can derive the formula

and many others such as:

12. Find by differentiating the equation two times. (Recall that is the second derivative of with respect to

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