How do you differentiate $y=csc^-1(3x)$ ?

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Answer 1 · 2016-11-25T21:07:07

Rewrite since $csc^-1$ is an inverse function.

$csc(y)=3x$

Differentiate both sides. On the left-hand side, don't forget that the chain rule will apply.

$-csc(y)cot(y)dy/dx=3$

Note that on the left-hand side, $csc(y)=3x$ . Also note that $cot(y)=sqrt(csc^2(y)-1)=sqrt(9x^2-1)$ .

$-3xsqrt(9x^2-1)dy/dx=3$

$dy/dx=-1/(xsqrt(9x^2-1))$

How do you differentiate y=csc^-1(3x)y=csc^-1(3x)?