- #1

dkotschessaa

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The problem I am having with these is that I'm sometimes not sure whether to begin differentiating first, or to start taking logarithms - and whether the order changes the outcome

For example:

Find the equation of the tangent line to the curve at the given point.

[tex] y= \frac{(e^x)}{x}[/tex]

At the points (1, e)

If I differentiate first I end up with [tex] y' = \frac{(e^x - 1)}{y}[/tex]. Plugging in the values to get the slope, I get [tex]m = \frac{(e-1)}{e}[/tex]

If I take logarithms of both sides prior to differentiating I get

[tex] dx/dy = y[\frac{1}{e^x} - 1(x)] [/tex]

which would give me a slope [tex]\frac{(e^2 - e)}{e} [/tex]

All of which are rather ugly things to be plugging into the point-slope form of the tangent line equation.

I suspect I'm doing something in the wrong order or missing a larger point.

-Dave K

For example:

Find the equation of the tangent line to the curve at the given point.

[tex] y= \frac{(e^x)}{x}[/tex]

At the points (1, e)

If I differentiate first I end up with [tex] y' = \frac{(e^x - 1)}{y}[/tex]. Plugging in the values to get the slope, I get [tex]m = \frac{(e-1)}{e}[/tex]

If I take logarithms of both sides prior to differentiating I get

[tex] dx/dy = y[\frac{1}{e^x} - 1(x)] [/tex]

which would give me a slope [tex]\frac{(e^2 - e)}{e} [/tex]

All of which are rather ugly things to be plugging into the point-slope form of the tangent line equation.

I suspect I'm doing something in the wrong order or missing a larger point.

-Dave K

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