Differentiation of trigonometric functions
Differentiating the inverse sine function

We let

Where

Then

Taking the derivative with respect to x {\displaystyle x} on both sides and solving for dy/dx:

Substituting cos y = 1 − sin 2 y {\displaystyle \cos y={\sqrt {1-\sin ^{2}y}}} in from above,

Substituting x = sin y {\displaystyle x=\sin y} in from above,
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