Question

If y=sin^(-1)⁡(x) then select the true statement.

(a) y2 = xy1^3

(b) y3 = xy2^3

(c) y2 = xy1^2

(d) y3 = xy1^2

The question was asked in homework.

My question is from The nth Derivative of Some Elementary Functions topic in chapter Differential Calculus of Engineering Mathematics

Answer 1

Correct answer is (a) y2 = xy1^3

To explain I would say: y=sin^-1⁡(x)

\(y_1=\frac{1}{\sqrt{1-x^2}}\)

\(y_2=\frac{x}{(1-x^2)^{3/2}}\)

\(y_2=\frac{x}{(1-x^2)^{3/2}} = xy_1^3\)