## Lammy 3 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

1. Annand

Take log of y and then differentiate... (dy/dx) at x=1 will give the slope of the tangent...

2. Lammy

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?

3. Annand

exactly

4. Lammy

is the slop -10.6063

5. Annand

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...

6. Annand

7. Lammy
8. Annand

is it not (1-pi)?

9. Lammy

yes yes thats the slope right? then how do i find the y to plug in for point slope form

10. Annand

you have the equation of the curve... put x=1 in it... that'll give you the point required...

11. Annand

that is y=X^(x^2) - X^(Pi) at x=1

12. Lammy

= 0

13. Annand

yep

14. Annand

so you've got a point and the slope... go on...

15. Lammy

can i leave it at y-0=1-pi(x-1)

16. Annand

y-0=(1-pi)(x-1) don't forget the brackets...

17. Lammy

thats it?

18. Annand

you may write it in the form y=mx+c if you like...

19. Lammy

y=-piX +X+pi-1

20. Annand

y=(1-pi)x-(1-pi)

21. Lammy

thank you soo much!

22. Annand

you're welcome...

23. Annand

A piece of advice: you should've calculated the derivative by hand....

24. Lammy

yea thats the problem i dont know how to do that one

25. Annand

do you want me to explain?

26. Lammy

27. Annand

In y=X^(x^2) - X^(Pi) the problem is with the first term... I believe that you know how to differentiate x^(pi)...

28. Lammy

yea

29. Annand

let y=p-q where p=X^(x^2) and q=X^(Pi)

30. Annand

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)]

31. Annand

y=dp/dx-dq/dx

32. Annand

got it?

33. Lammy

(1/p)dp/dx=x^2/x+2xlog(x)

34. Lammy

so derivative of log(x) = 2xlog(x)

35. Annand

nope... derivative of log(x) is 1/x

36. Annand

p is the product of x^2 and log(x) so you've to use the product rule.

37. Annand

\[d(x^2*\log(x))/dx=x^2*d(\log(x))/dx + \log(x)*d(x^2)/dx\]

38. Lammy

where is the 1/p from? (1/p)dp/dx=x^2/x+2xlog(x)

39. Lammy

where did the x^2 go? dp/dx=p[x+2xlog(x)]

40. Annand

x^2/x=x