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LilySwan
 9 months ago
find dy/dx if
(ax+cx^5)/kx^8
LilySwan
 9 months ago
find dy/dx if (ax+cx^5)/kx^8

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myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1a,c, and k are constants?

micahwood50
 9 months ago
Best ResponseYou've already chosen the best response.1Just use quotient rule.

LilySwan
 9 months ago
Best ResponseYou've already chosen the best response.0got stucked at one point

micahwood50
 9 months ago
Best ResponseYou've already chosen the best response.1\(\dfrac{d}{dx} \dfrac{f(x)}{g(x)} = \dfrac{f'(x)g(x)  f(x)g'(x)}{(g(x))^2}\)

LilySwan
 9 months ago
Best ResponseYou've already chosen the best response.0why can we solve the numerator part first

micahwood50
 9 months ago
Best ResponseYou've already chosen the best response.1treat constant as if they are just "number", and not variable.

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1@LilySwan Did you have a problem with finding derivative of the top or the bottom? That is what you need to plug into @micahwood50 's formula. what do you mean solve the numerator? You shouldn't be solving. You should be differentiating it. What is the derivative of the top part of your fraction?

LilySwan
 9 months ago
Best ResponseYou've already chosen the best response.0for the upper part 5cx^4 +a

micahwood50
 9 months ago
Best ResponseYou've already chosen the best response.1Right f'(x) = a+5cx^4

micahwood50
 9 months ago
Best ResponseYou've already chosen the best response.1Can you find g'(x)?

LilySwan
 9 months ago
Best ResponseYou've already chosen the best response.0for the lower part it will be 8kx^7

micahwood50
 9 months ago
Best ResponseYou've already chosen the best response.1Yep. So you have f(x) = ax+cx^5, f'(x) = a+5cx^4, g(x) = kx^8, g'(x) = 8kx^7 Just plug these in formula given above then simplify.

micahwood50
 9 months ago
Best ResponseYou've already chosen the best response.1Can you do it? @LilySwan

LilySwan
 9 months ago
Best ResponseYou've already chosen the best response.0i was told to use this formula \[\frac{ d }{ dx }(\frac{ u}{ v }) =\frac{ (v \frac{ du }{ dx })(u \frac{ dv }{ dx }) }{ v^2 }\]

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1same formula different notation

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1\[\dfrac{d}{dx} \dfrac{f(x)}{g(x)} = \dfrac{f'(x)g(x)  f(x)g'(x)}{(g(x))^2} \] if you want you can replace the f's with u's the g's with v's the ' things with d/dx and you have the same formula

LilySwan
 9 months ago
Best ResponseYou've already chosen the best response.0\[5cx^4+a.kx^8  ax+cx^5. 8kx^7/(kx^8)^2\]

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1\[\frac{(5cx^4+a)(kx^8)(ax+cx^5)(8kx^7)}{(kx^8)^2}\] i think this is what you mean

LilySwan
 9 months ago
Best ResponseYou've already chosen the best response.0what should i be doing the next

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1guess you could multiply things out on top and also use law of exponents on the bottom to simplify the bottom
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