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Unformatted text preview: , but you want it in terms of x . Let y be an angle of a right triangle. Since sin y = x , you can let the opposite side equal x and the hypotenuse equal one. Using the Pythagorean theorem, you can write cos y in terms of x . Now you have an expression for the derivative of arcsin x . It may seem strange that the derivative is not in terms of any of the other trig or inverse trig functions. If you remember that the trigonometric functions are all defined by right triangles, then the derivative makes more sense. If you use the same method as above, you can determine the derivatives of all the inverse trig functions. These derivatives may be difficult to memorize. But if you remember the method, then you can always derive them again....
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- Spring '10