anonymous
  • anonymous
find dy/dx if (ax+cx^5)/kx^8
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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myininaya
  • myininaya
a,c, and k are constants?
anonymous
  • anonymous
yes
anonymous
  • anonymous
Just use quotient rule.

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anonymous
  • anonymous
got stucked at one point
anonymous
  • anonymous
\(\dfrac{d}{dx} \dfrac{f(x)}{g(x)} = \dfrac{f'(x)g(x) - f(x)g'(x)}{(g(x))^2}\)
anonymous
  • anonymous
why can we solve the numerator part first
anonymous
  • anonymous
treat constant as if they are just "number", and not variable.
myininaya
  • myininaya
@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?
anonymous
  • anonymous
for the upper part 5cx^4 +a
anonymous
  • anonymous
Right f'(x) = a+5cx^4
anonymous
  • anonymous
Can you find g'(x)?
anonymous
  • anonymous
for the lower part it will be 8kx^7
anonymous
  • anonymous
Yep. 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.
anonymous
  • anonymous
Can you do it? @LilySwan
anonymous
  • anonymous
trying wait
anonymous
  • anonymous
i was told to use this formula \[\frac{ d }{ dx }(\frac{ u}{ v }) =\frac{ (v \frac{ du }{ dx })-(u \frac{ dv }{ dx }) }{ v^2 }\]
myininaya
  • myininaya
same formula different notation
anonymous
  • anonymous
?
myininaya
  • myininaya
\[\dfrac{d}{dx} \dfrac{f(x)}{g(x)} = \dfrac{f'(x)g(x) - f(x)g'(x)}{(g(x))^2} \] 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
anonymous
  • anonymous
\[5cx^4+a.kx^8 - ax+cx^5. 8kx^7/(kx^8)^2\]
myininaya
  • myininaya
\[\frac{(5cx^4+a)(kx^8)-(ax+cx^5)(8kx^7)}{(kx^8)^2}\] i think this is what you mean
anonymous
  • anonymous
yes
anonymous
  • anonymous
what should i be doing the next
myininaya
  • myininaya
guess you could multiply things out on top and also use law of exponents on the bottom to simplify the bottom

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