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Differentiating Inverse Trigonometric Functions

Ifthen we cannot finddirectly. Instead we take the sin of both sides to obtainand differentiate implicitly using the chain rule. We obtain

Since originallywas given as a function ofwe would normally findas a function ofWe can do this forusing the identityWe rearrange this to makethe subject:Hence

Ifthen we cannot finddirectly. Instead we take the cos of both sides to obtainand differentiate implicitly using the chain rule. We obtain

Since originallywas given as a function ofwe would normally findas a function ofWe can do this forusing the identityWe rearrange this to makethe subject:Hence

Ifthen we cannot finddirectly. Instead we take theof both sides to obtainand differentiate implicitly using the chain rule. We obtain

Since originallywas given as a function ofwe would normally findas a function ofWe can do this forusing the identity

Hence