Question

Equation of a tangent?
I never understood these

Answer 1

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Answer 2

evaluate the derivative then solve by plugging the coordinates

Answer 3

again, use quotient rule or product rule

Answer 4

Do you know what the tangent line is?

Answer 5

plug the coordinates into the slope-intercept form

Answer 6

So first I diff:
\[\LARGE y'=\frac{x(e^x)-(e^x)}{x^2}\]

Answer 7

Simplify:
\[\LARGE \frac{e^x(x-1)}{x^2}\]

Answer 8

Tagent line is given by: \[
y-f(a) = f'(a)(x-a)
\]In this case \(a=1\) and \(f(a) = e\).

Answer 9

plug in 1

Answer 10

So that makes it a horizontal line..

Answer 11

then now you have a slope of zero
to solve for the equation, use the slope-intercept form as @wio suggested

Answer 12

I mean point-slope form then convert it to slope-intercept form

Answer 13

So it would just turn out to be e?

Answer 14

most likely

Answer 15

Yea, it was, thanks nin :)

Answer 16

easy, right?

Answer 17

So far~

Answer 18

yeah get the general derivative solution first, then plug in the x-value (sometimes called a or x1), evaluate it and that will be your actual slope
after that, use the point-slope form using your slope and the (x1,y1) or (a, f(a))
convert it to y = mx+b or ax+by = c whichever is being asked