Question

find dy/dx if

(ax+cx^5)/kx^8

Answer 1

a,c, and k are constants?

Answer 2

yes

Answer 3

Just use quotient rule.

Answer 4

got stucked at one point

Answer 5

\(\dfrac{d}{dx} \dfrac{f(x)}{g(x)} = \dfrac{f'(x)g(x) - f(x)g'(x)}{(g(x))^2}\)

Answer 6

why can we solve the numerator part first

Answer 7

treat constant as if they are just "number", and not variable.

Answer 8

@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?

Answer 9

for the upper part 5cx^4 +a

Answer 10

Right f'(x) = a+5cx^4

Answer 11

Can you find g'(x)?

Answer 12

for the lower part it will be 8kx^7

Answer 13

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.

Answer 14

Can you do it? @LilySwan

Answer 15

trying wait

Answer 16

i was told to use this formula
\[\frac{ d }{ dx }(\frac{ u}{ v }) =\frac{ (v \frac{ du }{ dx })-(u \frac{ dv }{ dx }) }{ v^2 }\]

Answer 17

same formula
different notation

Answer 18

?

Answer 19

\[\dfrac{d}{dx} \dfrac{f(x)}{g(x)} = \dfrac{f'(x)g(x) - f(x)g'(x)}{(g(x))^2} \]
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

Answer 20

\[5cx^4+a.kx^8 - ax+cx^5. 8kx^7/(kx^8)^2\]

Answer 21

\[\frac{(5cx^4+a)(kx^8)-(ax+cx^5)(8kx^7)}{(kx^8)^2}\]
i think this is what you mean

Answer 22

yes

Answer 23

what should i be doing the next

Answer 24

guess you could multiply things out on top
and also use law of exponents on the bottom to simplify the bottom