Inverse Trigonometric Functions Are the derivatives of the inverse trigonometric functions algebraic or transcendental functions?...

Step 1
Given:
Are the derivatives of the inverse trigonometric functions algebraic or transcendental functions? Explain.
Step 2
The derivative of inverse trignometric function are algebraic.
$\frac{d}{dx}[\arcsin u]=\frac{u^{{}^{\prime }}}{\sqrt{1-u^2}}$
$\frac{d}{dx}[\arccos u]=\frac{-u^{{}^{\prime }}}{\sqrt{1-u^2}}$
$\frac{d}{dx}[\arctan u]=\frac{u^{{}^{\prime }}}{1+u^2}$
$\frac{d}{dx}\left[arсcotu\right]=\frac{-u^{{}^{\prime }}}{1+u^2}$
$\frac{d}{dx}\left[arсsecu\right]=\frac{u^{{}^{\prime }}}{\mid u\mid \sqrt{u^2-1}}$
$\frac{d}{dx}\left[arсcscu\right]=\frac{-u^{{}^{\prime }}}{\mid u\mid \sqrt{u^2-1}}$
The derivative of inverse trignometric function are algebraic.