The derivative of \(\displaystyle{\arcsin{{\left({x}\right)}}}\) at \(\displaystyle{x}={1}\) Why

Isaac Hampton

Isaac Hampton

Answered question


The derivative of arcsin(x) at x=1
Why the derivative of arcsin(x) isn't defined at x=1? The functional value of arcsin(x) seems to grow faster around 1, but there is no discontinuity. So, why the slope is undefined?

Answer & Explanation

Abdullah Avery

Abdullah Avery

Beginner2022-04-04Added 19 answers

The tangent line becomes vertical as x approaches 1, and vertical lines have undefined slope. This corresponds to sinx having a horizontal tangent (slope 0) at π2

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