Inverse Trigonometric Functions - GRE Subject Test: Math

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Question

Evaluate the derivative $\frac{\mathrm{d} }{\mathrm{d} x} sin^{-1}(x)$

Answer

The inverse trig functions should be memorized.

$\frac{\mathrm{d} }{\mathrm{d} x} sin^{-1}(x)=\frac{1}{\sqrt{1-x^2}}$

The other common inverse trig functions are

$\frac{\mathrm{d} }{\mathrm{d} x} cos^{-1}(x)=-\frac{1}{\sqrt{1-x^2}}$

$\frac{\mathrm{d} }{\mathrm{d} x} tan^{-1}(x)=\frac{1}{1+x^2}$

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