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find the equation of the tangent to the curve y=X^(x^2)  X^(Pi) where x=1 find the equation of the tangent to the curve y=X^(x^2)  X^(Pi) where x=1 @Mathematics
 2 years ago
 2 years ago
find the equation of the tangent to the curve y=X^(x^2)  X^(Pi) where x=1 find the equation of the tangent to the curve y=X^(x^2)  X^(Pi) where x=1 @Mathematics
 2 years ago
 2 years ago

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AnnandBest ResponseYou've already chosen the best response.1
Take log of y and then differentiate... (dy/dx) at x=1 will give the slope of the tangent...
 2 years ago

LammyBest ResponseYou've already chosen the best response.0
when you say dy/dx at x=1 do you mean to plug in 1 for all x after i get the derivative of the equation?
 2 years ago

AnnandBest ResponseYou've already chosen the best response.1
you can also find y at x=1... Thus you know the slope and one point in the line which will help you to find the equation...
 2 years ago

LammyBest ResponseYou've already chosen the best response.0
http://www.wolframalpha.com/input/?i=derivative+x%5E%28x%5E2%29x%5E%28%CF%80%29
 2 years ago

LammyBest ResponseYou've already chosen the best response.0
yes yes thats the slope right? then how do i find the y to plug in for point slope form
 2 years ago

AnnandBest ResponseYou've already chosen the best response.1
you have the equation of the curve... put x=1 in it... that'll give you the point required...
 2 years ago

AnnandBest ResponseYou've already chosen the best response.1
that is y=X^(x^2)  X^(Pi) at x=1
 2 years ago

AnnandBest ResponseYou've already chosen the best response.1
so you've got a point and the slope... go on...
 2 years ago

LammyBest ResponseYou've already chosen the best response.0
can i leave it at y0=1pi(x1)
 2 years ago

AnnandBest ResponseYou've already chosen the best response.1
y0=(1pi)(x1) don't forget the brackets...
 2 years ago

AnnandBest ResponseYou've already chosen the best response.1
you may write it in the form y=mx+c if you like...
 2 years ago

AnnandBest ResponseYou've already chosen the best response.1
A piece of advice: you should've calculated the derivative by hand....
 2 years ago

LammyBest ResponseYou've already chosen the best response.0
yea thats the problem i dont know how to do that one
 2 years ago

AnnandBest ResponseYou've already chosen the best response.1
do you want me to explain?
 2 years ago

AnnandBest ResponseYou've already chosen the best response.1
In y=X^(x^2)  X^(Pi) the problem is with the first term... I believe that you know how to differentiate x^(pi)...
 2 years ago

AnnandBest ResponseYou've already chosen the best response.1
let y=pq where p=X^(x^2) and q=X^(Pi)
 2 years ago

AnnandBest ResponseYou've already chosen the best response.1
taking log of p log(p)=x^2*log(x) then differentiate (1/p)dp/dx=x^2/x+2xlog(x) dp/dx=p[x+2xlog(x)] dp/dx=x^(x^2)*[x+2xlog(x)]
 2 years ago

LammyBest ResponseYou've already chosen the best response.0
(1/p)dp/dx=x^2/x+2xlog(x)
 2 years ago

LammyBest ResponseYou've already chosen the best response.0
so derivative of log(x) = 2xlog(x)
 2 years ago

AnnandBest ResponseYou've already chosen the best response.1
nope... derivative of log(x) is 1/x
 2 years ago

AnnandBest ResponseYou've already chosen the best response.1
p is the product of x^2 and log(x) so you've to use the product rule.
 2 years ago

AnnandBest ResponseYou've already chosen the best response.1
\[d(x^2*\log(x))/dx=x^2*d(\log(x))/dx + \log(x)*d(x^2)/dx\]
 2 years ago

LammyBest ResponseYou've already chosen the best response.0
where is the 1/p from? (1/p)dp/dx=x^2/x+2xlog(x)
 2 years ago

LammyBest ResponseYou've already chosen the best response.0
where did the x^2 go? dp/dx=p[x+2xlog(x)]
 2 years ago
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