Inverse trig functions and their derivatives
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20 Terms
f(x) = \sin^{-1}(x)
f'(x) = \frac{1}{\sqrt{1-x^{2}}}
f(x) = \cos^{-1}(x)
f'(x) = -\frac{1}{\sqrt{1-x^{2}}}
f(x) = \tan^{-1}(x)
f'(x) = \frac{1}{1+x^{2}}
f(x) = \cot^{-1}(x)
f'(x) = -\frac{1}{1+x^{2}}
f(x) = \sec^{-1}(x)
f'(x) = \frac{1}{|x|\sqrt{x^{2}-1}}
f(x) = \csc^{-1}(x)
f'(x) = -\frac{1}{|x|\sqrt{x^{2}-1}}
f(x) = \sinh^{-1}(x)
f'(x) = \frac{1}{\sqrt{x^{2}+1}}
f(x) = \cosh^{-1}(x)
f'(x) = \frac{1}{\sqrt{x^{2}-1}}
f(x) = \tanh^{-1}(x)
f'(x) = \frac{1}{1-x^{2}}, \quad |x| < 1
f(x) = \coth^{-1}(x)
f'(x) = \frac{1}{1-x^{2}}, \quad |x| > 1
f(x) = \text{sech}^{-1}(x)
f'(x) = -\frac{1}{x\sqrt{1-x^{2}}}
f(x) = \text{csch}^{-1}(x)
f'(x) = -\frac{1}{|x|\sqrt{1+x^{2}}}
f(x) = \sec^{-1}(x)
f'(x) = \frac{1}{|x|\sqrt{x^{2}-1}}
f(x) = \csc^{-1}(x)
f'(x) = -\frac{1}{|x|\sqrt{x^{2}-1}}
f(x) = \sinh^{-1}(x)
f'(x) = \frac{1}{\sqrt{x^{2}+1}}
f(x) = \cosh^{-1}(x)
f'(x) = \frac{1}{\sqrt{x^{2}-1}}
f(x) = \tanh^{-1}(x)
f'(x) = \frac{1}{1-x^{2}}, \quad |x| < 1
f(x) = \coth^{-1}(x)
f'(x) = \frac{1}{1-x^{2}}, \quad |x| > 1
f(x) = \text{sech}^{-1}(x)
f'(x) = -\frac{1}{x\sqrt{1-x^{2}}}
f(x) = \text{csch}^{-1}(x)
f'(x) = -\frac{1}{|x|\sqrt{1+x^{2}}}
Note 
Flashcards (33)