Tyra

2021-10-12

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

d2saint0

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.
$\frac{d}{dx}\left[\mathrm{arcsin}u\right]=\frac{{u}^{{}^{\prime }}}{\sqrt{1-{u}^{2}}}$
$\frac{d}{dx}\left[\mathrm{arccos}u\right]=\frac{-{u}^{{}^{\prime }}}{\sqrt{1-{u}^{2}}}$
$\frac{d}{dx}\left[\mathrm{arctan}u\right]=\frac{{u}^{{}^{\prime }}}{1+{u}^{2}}$
$\frac{d}{dx}\left[arсcotu\right]=\frac{-{u}^{{}^{\prime }}}{1+{u}^{2}}$
$\frac{d}{dx}\left[arсsecu\right]=\frac{{u}^{{}^{\prime }}}{\mid u\mid \sqrt{{u}^{2}-1}}$
$\frac{d}{dx}\left[arсcscu\right]=\frac{-{u}^{{}^{\prime }}}{\mid u\mid \sqrt{{u}^{2}-1}}$
The derivative of inverse trignometric function are algebraic.

Do you have a similar question?