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zeesbrat3
 one year ago
Determine the slope of the graph of x4 = ln(xy) at the point (1, e).
zeesbrat3
 one year ago
Determine the slope of the graph of x4 = ln(xy) at the point (1, e).

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freckles
 one year ago
Best ResponseYou've already chosen the best response.3find the slope by first differentiating both sides of the given equation

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0But hot can you find the derivative of e?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3why do you want the derivative of e? by the way e is a constant and derivative of e is 0. But why do you need this information?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[\frac{d}{dx}x^4=? \\ \frac{d}{dx}\ln(xy)=?\] the first can be found by using power rule second can be found using chain rule and product rule

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0Sorry, I'm just confused as to how to solve for the answer.. This question is on a practice test so I need to learn how to do it for the actual test.

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0So the first would be \[4x^3\] And the second would be \[\frac{ d }{ dx } \ln x + \ln y\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3oh okay so you used product rule for log but you still need to differentiate that sum: \[\frac{d}{dx}(\ln(x)+\ln(y)) \\ =\frac{d}{dx}\ln(x)+\frac{d}{dx}\ln(y)\] =?

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ y }{ x }\]?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3do you know that: where u is a function of x that: \[\frac{d}{dx}\ln(u)= \frac{u'}{u}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[\frac{d}{dx}\ln(x)=\frac{(x)'}{x}=\frac{1}{x} \\ \frac{d}{dx}\ln(y)=\frac{y'}{y}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[x^4=\ln(xy) \\ \text{ after differentiating both sides we have } \\ 4x^3=\frac{1}{x}+\frac{y'}{y} \] now you can replace x with 1 and y with e and solve for y' (the slope at (1,e))

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0So \[4x^3 = 1 + \frac{ y' }{ e }\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.3close you need to replace all the x's with 1

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0Ooo whoops! \[4 = 1 + \frac{ y' }{ }\]

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0theres supposed to be an e under the y prime

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[4=1+\frac{y'}{e}\] yep now just solve for y' (this will be the slope at (1,e) since we replaced x with 1 and y with e)

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0Thank you! Would you mind helping me with one more? Logs through me for a loop

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0Thanks! \[\frac{ d }{ dx }[x^3e^x] = x^2e^x(3x+2)\]

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0I have to find whether that is true or not

freckles
 one year ago
Best ResponseYou've already chosen the best response.3well do you know product rule?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3x^3e^x is a product of x^3 and e^x

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[\frac{d}{dx}(x^3e^x)=e^x \frac{d}{dx}x^3+x^3 \frac{d}{dx}e^x\] what are the following: \[\frac{d}{dx}x^3=? \\ \frac{d}{dx}e^x=?\]

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0Right. So the first is \[3x^2\] and the second is 0?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3the second is not 0 e^x is not a constant

freckles
 one year ago
Best ResponseYou've already chosen the best response.3for example e^2 and e^3 aren't the same so there is no way e^x remains the same

freckles
 one year ago
Best ResponseYou've already chosen the best response.3the derivative of e^x is e^x

zeesbrat3
 one year ago
Best ResponseYou've already chosen the best response.0Because it is a constant?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3I thought I just said it wasn't a constant and gave a reason why it wasn't a constant. e is a constant e^x is not a constant (it varies) (Example: e^2 is not the same as e^3)
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