Log Quesiton help please! (1 Viewer)

ad_321 · Mar 5, 2016

Differentiate x^3loge(x+1)

How do you solve this? Thankyou

InteGrand · Mar 5, 2016

ad_321 said:
Differentiate x^3loge(x+1)

How do you solve this? Thankyou

$\noindent Let $y = x^3 \ln (x+1)$. Then using the product rule, the derivative is$

$\begin{align*} y^\prime &= 3x^2 \ln (x+1) + x^3\cdot \frac{1}{x+1} \\ &= 3x^2 \ln (x+1) +\frac{x^3}{x+1}.\end{align*}$

ad_321 · Mar 5, 2016

InteGrand said:
$\noindent Let $y = x^3 \ln (x+1)$. Then using the product rule, the derivative is$

$\begin{align*} y^\prime &= 3x^2 \ln (x+1) + x^3\cdot \frac{1}{x+1} \\ &= 3x^2 \ln (x+1) +\frac{x^3}{x+1}.\end{align*}$

Thanks! Can you also do this one:

loge(loge^x)

kawaiipotato · Mar 5, 2016

ad_321 said:
Thanks! Can you also do this one:

loge(loge^x)

$$ let $ y = \ln (\ln \left(e^{x}\right))$

$$ then $ y = \ln (x \ln e )$

$= \ln x$

$$so$ y' = \frac{1}{x}$

ad_321 · Mar 6, 2016

if you have just log base e how do you differentiate it

KingOfActing · Mar 6, 2016

ad_321 said:
if you have just log base e how do you differentiate it

$\log_e{x} \stackrel{\text{def.}}{=} \ln{x}$

Nailgun · Mar 6, 2016

ad_321 said:
if you have just log base e how do you differentiate it

d/dx logex = 1/x

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Log Quesiton help please! (1 Viewer)

ad_321

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InteGrand

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ad_321

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kawaiipotato

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KingOfActing

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