<p>So basically, I got this WS near the end of the year about inverse functions and the relations between their derivatives? Can anybody explain this to me and if it will actually be on the AP exam?</p>
<p>from what i've seen in my review book, it may only come up in a multiple choice, no big deal</p>
<p>Know arcsin and arctan.</p>
<p>dy/dx of arcsin(u) is (du/dx)<em>1/sqrt(1-u^2)
dy/dx of arctan(u) is (du/dx)</em>1/1+u^2</p>
<p>arctan is important.</p>
<p>I think I was a bit unclear. I was asking about something different. i don't remember the exact problems, but it is something like this:</p>
<p>**g(x) is the inverse function of f(x). What is g'(3)?</p>
<p>They give you a table of values for f(x) and f'(x) at different x-values.**</p>
<p>I reread my first post and it was actually pretty clear, so read that, not just the title.</p>
<p>For the example you gave:
1. Find what value of x gives you f(x) = 3
2. g'(3) is then just 1/f'(x) using whatever the x was you found in step 1</p>
<p>let me try this. Here is the table I made up:
X . f(x) . f'(x)
5 .. 7 .... 8
4 .. 3 .... 9</p>
<p>g'(3)=1/9</p>
<p>Correct?</p>
<p>no.</p>
<p>if g(x) is the inverse function of f(x) then all the x values are g(x) values and all the f(x) values are x values for g(x), same goes for g'(x) x,f'(x) -> f'(x),x on g'(x)</p>
<p>yes, g'(3)=1/9. or well atleast it should.</p>
<p>because dy/dx=1/(dx/dy). so if f(x) is equal to y, then f'(x) or y' is equal to dy/dx. however the inverse of f(x) is basically with in terms of x instead of y. so the derivative of the inverse of f(x) is dx/dy.</p>
<p>based on the previous information.</p>
<p>9=1/(1/9) so the (1/9) part is basically dx/dy or the derivative of the inverse function.</p>
<p>@x9521</p>
<p>I don't think you are correct because I specifically remember the teacher talking about reciprocals.</p>
<p>@aznpride9264</p>
<p>Ah, that made it so much easier to understand (talking about dy/dx=1(1dx/dy)).</p>
<p>If you don't want to memorize, it is easy to derive:</p>
<p>If you use that if g(x) is the inverse of f(x), then:</p>
<p>g( f(x) ) = x</p>
<p>Using the chain rule:</p>
<p>g'( f(x) ) * f'(x) = 1</p>
<p>Divide:</p>
<p>g'( f(x) ) = 1 / f'(x)</p>
<p>So if it wants g'(3), you need to plug in 3 for f(x)and then, using 3 = f(x), solve for x. Then, plug in.</p>
<p>"from what i've seen in my review book, it may only come up in a multiple choice, no big deal"</p>
<p>Actually, if I recall correctly, wasn't there a question regarding inverses and derivatives on the AB Free Response last year? I remember drawing a complete blank on that one</p>
<p>formula for inverse</p>
<p>1/f'(f^-1(x))</p>
<p>"Actually, if I recall correctly, wasn't there a question regarding inverses and derivatives on the AB Free Response last year? I remember drawing a complete blank on that one"</p>
<p>Yeah, I remember that too.</p>
<p>^^^ yea that was the question where the avg score was .9 out of 9</p>
<p>so sad</p>
<p>@diamondbacker</p>
<p>Thanks. That makes it even clearer.</p>