Inverse Trig function derivative

EvilBunny
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Homework Statement



Let

arctan (\sqrt{3x^2 -1})


then dy/dx


Well I know that the derivative of arctanx is

1/ 1 + x ² but when I got something other then simply x I don't know how to proceed
 
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x=the radical

example

y=\arctan{(x^2)}

y'=\frac{2x}{1+(x^2)^2}
 
Neat I get it, thanks.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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