Question

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(?) log(Sin~Tz) (0 < <1)
(8) Tan~「(Z2)

Answer 1

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えだまめ🫛

(7)
x = siny とすると　dx = cosy･dy

d{log(sin⁻¹x)}/dx
= d{log(y)}/dx
= 1/y･dy/dx
= 1/y･1/cosy
= 1/(y･cosy)
= 1/{sin⁻¹x･cos(sin⁻¹x)}

(8)
x² = tany とすると　2xdx = 1/cos²y･dy

d{tan⁻¹(x²)}/dx
= dy/dx
= 2x･cos²y
= 2x･cos²{tan⁻¹(x²)}