Derivative of e^(1+lnx): Solving for y

Thread starter Juwad
Start date Nov 8, 2006
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Derivative

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To solve the derivative of y = e^(1 + ln x), the user correctly applies the natural logarithm to both sides, leading to the equation lny * y' = (1 + ln x). They then derive y' as e^(1 + ln x) * (1/x), simplifying it to y' = (e * x) / x = e. The user successfully rewrites e^(1 + ln x) as e * x, confirming their understanding of the relationship between the exponential and logarithmic functions. The discussion emphasizes the importance of applying logarithmic properties correctly in differentiation.

Nov 8, 2006

Juwad

hello,

i need some assistance on this problem:

y = e^(1+lnx)

1st. I brought down the (1+lnx) by using natural log on both sides.

lny*y'=(1+lnx)*lne
y'/y=(1/x)*1

y'=e^(1+lnx)*(1/x)

what do i do next?

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Nov 8, 2006

quasar987

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e^{1+\ln x}=e^1e^{\ln x}=ex

Nov 8, 2006

Juwad

thanks,!

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