What is the next step

find the derivative of: (5e^-x - 3) / (5e^-x + 3)

rule: u'v - uv' / v^2

what I did:

(5e^-x - 3) / (5e^-x + 3)
[ (-5e^-x)(5e^-x + 3) ] - [ (5e^-x - 3)(-5e^-x) ] / (5e^-x + 3)^2
What do I do here?

Factor out −5e^-x in numerator:

= [(−5e^-x) ((5e^-x + 3) - (5e^-x - 3))] / (5e^-x + 3)^2

= [(−5e^-x) (5e^-x + 3 - 5e^-x + 3)] / (5e^-x + 3)^2

= (−5e^-x) (6) / (5e^-x + 3)^2

= −30e^-x / (5e^-x + 3)^2

Now multiply numerator and denominator by e^(2x) = (e^x)^2

= −30e^-x * e^(2x) / ((5e^-x + 3) * e^x)^2

= −30e^x / (5 + 3 e^x)^2

You can still simplify from here but it would be easier to rewrite the problem ( it has negative exponents, so multiply by e^x/e^x)

So y =(5-3e^x)/(5+3e^x)

Y'=(5+3e^x)(-3e^x)-(5-3e^x)(3e^x)
......--------------------------------…
(5+3e^x)^2

=-15e^x-9e^2x-15e^x+9e^2x
-----------------------------------
Same denom

=( -30e^x)/(5+3e^x)^2

diff((5*exp(-x)-3)/(5*exp(-x)+3), x)

-5*exp(-x)/(5*exp(-x)+3)+(5*(5*exp(-x)…

simplify(-5*exp(-x)/(5*exp(-x)+3)+(5*(… = -30*exp(-x)/(5*exp(-x)+3)^2

Simplify!