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Derivatives and Inverse Functions: Complete Table, Graphs & Tangent Line

Learn how to complete tables for sinx, convert values, sketch graphs for sinx and arcsinx, find values and draw tangent lines for f-1(a), and explore inverse trig functions and their derivatives.

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Derivatives and Inverse Functions: Complete Table, Graphs & Tangent Line

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  1. Derivatives and Inverse Functions • 1. Complete the table (without a calculator) for f(x) = sinx • 2. Convert both the x- and y- values from your table to the nearest tenth. • 3. Use the tables above to produce a table for f-1(x) = arcsinx • Use the tables to sketch the graphs of f(x) = sin x and f-1(x) = arcsinx • Find the values of (f-1)’(a) if given f(X)=sinx where a= • Draw the tangent line to (f-1)(a) at a=

  2. Inverse Trig Functions and Derivatives Function: y = arcsinx The derivative formula: Graph: Domain: Range: Function: y = arctanx Graph: The derivative formula: Domain: Range: Function: y = arcsecx Graph: The derivative formula: Domain: Range:

  3. Function: y = arccosx Graph: The derivative formula: Domain: Range: Function: y = arccotx Graph: The derivative formula: Domain: Range: The derivative formula: Function: y = arccscx Graph: Domain: Range:

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