At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
Take log of y and then differentiate... (dy/dx) at x=1 will give the slope of the tangent...
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?
is the slop -10.6063
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...
what was your dy/dx
is it not (1-pi)?
yes yes thats the slope right? then how do i find the y to plug in for point slope form
you have the equation of the curve... put x=1 in it... that'll give you the point required...
that is y=X^(x^2) - X^(Pi) at x=1
so you've got a point and the slope... go on...
can i leave it at y-0=1-pi(x-1)
y-0=(1-pi)(x-1) don't forget the brackets...
you may write it in the form y=mx+c if you like...
thank you soo much!
A piece of advice: you should've calculated the derivative by hand....
yea thats the problem i dont know how to do that one
do you want me to explain?
In y=X^(x^2) - X^(Pi) the problem is with the first term... I believe that you know how to differentiate x^(pi)...
let y=p-q where p=X^(x^2) and q=X^(Pi)
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)]
so derivative of log(x) = 2xlog(x)
nope... derivative of log(x) is 1/x
p is the product of x^2 and log(x) so you've to use the product rule.
\[d(x^2*\log(x))/dx=x^2*d(\log(x))/dx + \log(x)*d(x^2)/dx\]
where is the 1/p from? (1/p)dp/dx=x^2/x+2xlog(x)
where did the x^2 go? dp/dx=p[x+2xlog(x)]