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anonymous
 one year ago
find the derivative of the function: x arctan x=e^y at the point (1, ln pi/4)
anonymous
 one year ago
find the derivative of the function: x arctan x=e^y at the point (1, ln pi/4)

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freckles
 one year ago
Best ResponseYou've already chosen the best response.4to differentiate x*arctan(x) (w.r.t x) you nee to apply product rule to differentiate e^y (w.r.t x) use chain rule

sweetburger
 one year ago
Best ResponseYou've already chosen the best response.1you could make x=e^y ln(x)=y

freckles
 one year ago
Best ResponseYou've already chosen the best response.4@sweetburger what do you mean?

sweetburger
 one year ago
Best ResponseYou've already chosen the best response.1converting exponential to logarthimic they are equivalent... unless I am wrong idk

sweetburger
 one year ago
Best ResponseYou've already chosen the best response.1just trying to help

sweetburger
 one year ago
Best ResponseYou've already chosen the best response.1a^y=x equal loga(x)=y

freckles
 one year ago
Best ResponseYou've already chosen the best response.4\[x \arctan(x)=e^y \\ \text{ differentiate both sides w.r.t. } x \\ \frac{d}{dx}(x \arctan(x))= \frac{d}{dx}(e^y) \\ \] oh are you saying she can write: \[\ln(x \arctan(x))=y \text{ instead of } x \arctan(x)=e^y\] ok I was just confused because we don't have the equation x=e^y

sweetburger
 one year ago
Best ResponseYou've already chosen the best response.1well my bad I completely read teh question wrong I thought it was 2 different equations that we were taking the derivative of... my bad

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I don't understand what (w.r.t.x) means

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohh ok so find the derivative of x arctanx x and then e^y the apply the product rule and then the chain rule I am looking for the inverse tho

sweetburger
 one year ago
Best ResponseYou've already chosen the best response.1so wrtx is basically differentiating both sides with respect to x or (d/dx) of both sides?

freckles
 one year ago
Best ResponseYou've already chosen the best response.4\[\frac{d}{dx} \arctan(x)=\frac{1}{1+x^2}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.4is that what you mean @meaghan25

freckles
 one year ago
Best ResponseYou've already chosen the best response.4derivative of that inverse function

freckles
 one year ago
Best ResponseYou've already chosen the best response.4\[\frac{d}{dx}e^x=e^x \\ \frac{d}{dx}e^u=\frac{du}{dx} e^u \text{ where} u=u(x)\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.4now all you have to really do is replace u with y and apply that product rule I was talking about

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes I need the inverse

freckles
 one year ago
Best ResponseYou've already chosen the best response.4yes d/dx means differentiating w.r.t x

freckles
 one year ago
Best ResponseYou've already chosen the best response.4what do you need the inverse of ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sorry I hate open study cus of the typing issue I have with it but the directions say finding dy/dx at a point. in exercises 19 22, find dy/dx at the given point for the equation 21. x arctan x = e^y , (1, lnpi/4) does that mean I need to find the inverse of the function or just the derivative of dy/dx.

freckles
 one year ago
Best ResponseYou've already chosen the best response.4the question says nothing about finding the inverse of anything \[x \arctan(x)=e^y \\ \text{ differentiate both sides w.r.t. x} \\ \frac{d}{dx} x \arctan(x)=\frac{d}{dx}e^y \\ \text{ apply product rule on left hand side } \\ x \frac{d}{dx} \arctan(x)+\arctan(x) \frac{d}{dx} x=\frac{d}{dx}e^y \\ \text {apply chain rule to right hand side } \\ x \frac{d}{dx} \arctan(x)+\arctan(x)\frac{d}{dx}x=\frac{dy}{dx} e^y\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.4dy/dx means find the derivative of the y w.r.t. x

freckles
 one year ago
Best ResponseYou've already chosen the best response.4you need to replace d/dx arctan(x) and replace d/dx x with arctan(x)'s derivative and x's derivative respectively

freckles
 one year ago
Best ResponseYou've already chosen the best response.4anyways once you are done enter in your point and solve for dy/dx and you are done

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok thank you so much

freckles
 one year ago
Best ResponseYou've already chosen the best response.4do you want me to check your answer?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no I have the answer already just couldn't figure out what I needed to do exactly

courtneygraley009
 one year ago
Best ResponseYou've already chosen the best response.0Try this online calculator to solve the problem http://www.acalculator.com/quadraticequationcalculatorformulasolver.html I hope it is helpful.
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