Question

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

Answer 1

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

Answer 2

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?

Answer 3

exactly

Answer 4

is the slop -10.6063

Answer 5

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...

Answer 6

what was your dy/dx

Answer 7

http://www.wolframalpha.com/input/?i=derivative+x%5E%28x%5E2%29-x%5E%28%CF%80%29

Answer 8

is it not (1-pi)?

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

= 0

Answer 13

yep

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

thats it?

Answer 18

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

Answer 19

y=-piX +X+pi-1

Answer 20

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

Answer 21

thank you soo much!

Answer 22

you're welcome...

Answer 23

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

Answer 24

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

Answer 25

do you want me to explain?

Answer 26

yes please

Answer 27

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

Answer 28

yea

Answer 29

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

Answer 30

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)]

Answer 31

y=dp/dx-dq/dx

Answer 32

got it?

Answer 33

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

Answer 34

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

Answer 35

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

Answer 36

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

Answer 37

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

Answer 38

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

Answer 39

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

Answer 40

x^2/x=x