3/10/2024 0 Comments Derivative of arctan□= 1 □ ′ □ 0 □+ □ 0 □ ′ □ 0 −□ □ 0 □ ′ □ 0 The slopes are reciprocals This gives us a hint about the relationship between the derivative of a function and its inverse (when an inverse exists) The next theorem asserts the existence of the derivative of inverse function (without proof) In addition, the relationship is given and can be proven using the Chain Rule How are the slopes of the tangent lines from the previous slide related? The slope of the tangent line at ( □ 0, □ 0 ) for □ is □= □ ′ □ 0 □− □ 0 +□( □ 0 ) Since the tangent line at ( □ 0, □ 0 ) for □ is a reflection of the above tangent line, we can find its equation in terms of □′ by swapping □ and □, then solving for □ □= □ ′ □ 0 □− □ 0 +□ □ 0 □= 1 □ ′ □ 0 □+ □ 0 □ ′ □ 0 −□ □ 0 □ ′ □ 0 ![]() Presentation on theme: "Derivatives of Inverse Trigonometric Functions"- Presentation transcript:ġ Derivatives of Inverse Trigonometric Functions
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