Question

Find the derivative. Show all steps please.
y=[x3-3x2+5x]/[5x]

Answer 1

do u mean [x^3-3x^2+5x]/[5x]?

Answer 2

ya

Answer 3

y=[x3-3x2+5x]/[5x] = x^2 /5 - 3x/5 +1
y' = 2x/5 - 3/5

Answer 4

you skipped some steps that i m getting confused about

Answer 5

One way to look at this, other than @Callisto 's, albeit his is easier, is to factor out the 1/5 and apply the quotient rule or the inverse product rule.

Answer 6

i need to use quotient rule

Answer 7

the function can be written as

\[y=\frac{x^3}{5x} -\frac{3x^2}{5x} + \frac{5x}{5x}\]

then simplifying it gives Callisto's solution

Answer 8

oh ok i get it now :) thanks you guys!

Answer 9

\[y=\frac{x^3-3x^2+5x}{5x} =\frac{5x \frac{d}{dx}(x^3-3x^2+5x) -(x^3-3x^2+5x)\frac{d}{dx} (5x) }{(5x)^2} \]\[=\frac{5x(3x^2 - 6x+5) - 5(x^3-3x^2+5x)}{25x^2}= \frac{5x(3x^2 - 6x+5) - 5x(x^2-3x+5)}{25x^2}\]\[= \frac{(3x^2 - 6x+5) -(x^2-3x+5)}{5x}=\frac{(2x^2 - 3x)}{5x}= 2x/3 - 3/5\]
I didn't know you need to use quotient rule :|

Answer 10

Wait... for the second equal sign, please add ' y' ' in front of it :|
Sorry

Answer 11

1st fraction in the final answer should read

2x/5

Answer 12

i think u dont need to put 25x^2 rahter (5x)^2

Answer 13

And for the answer, it is 2x/5 - 3/5

Answer 14

anyhow the quote rule is right

Answer 15

nice job on the quotient rule.. Callisto... shows why you try to simplify 1st

Answer 16

i applaud you castillo

Answer 17

If I simplify it... I won't don't need to use quotient rule and everything becomes simple!!!!!!!!
\[y=\frac{x^3-3x^2+5x}{5x} = \frac{x^2}{5} - \frac{3x}{5} +1\]\[y' = 2x/5 - 3/5 \]