Find the Derivatives of the Following Functions:
(A) $f ( x ) = \sin ^ { - 1 } \left( x ^ { 2 } \right)$

question 44

Essay

Find the derivatives of the following functions:
(a) $f ( x ) = \sin ^ { - 1 } \left( x ^ { 2 } \right)$ (b) $f ( x ) = \left( \sin ^ { - 1 } x \right) ^ { 2 }$ (c) $f ( x ) = x \sin ^ { - 1 } \left( x ^ { 3 } \right)$ (d) $f ( x ) = \tan ^ { - 1 } \left( \frac { x + 1 } { x - 1 } \right)$ (e) $f ( x ) = \cos ^ { - 1 } \left( e ^ { x } \right)$

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Income

The money received by a person or household from various sources like work, investments, or benefits, typically used for consumption, savings, and investing.

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The value of an ownership interest in property, including shareholders' equity in a corporation, representing assets minus liabilities.

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The optimal allocation of resources to maximize the production of goods and services, ensuring that these are distributed in the most effective manner.

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The legal framework and methodologies used by governments to assess and collect taxes from individuals and organizations.