Help w/ Derivatives.

#1
This is the equation

y=42 * (126/((x+168)) ^2

do i use the chain formula? or..

I'm not sure. I appreciate it very much if someone can help me.
:)
 

JohnM

TS Contributor
#2
First use the chain rule for the portion with the exponent, then the fraction needs the quotient rule, then the main product (42 * ( )/( )) needs the product rule.
 
#3
Michelle,

john is in general correct, but i would approach this problem differently and teach my calc students the same:


y=42 * (126/((x+168)) ^2
y= 42*(126*(x+168)^-1)^2

let U= 126*(x+168)^-1
then dU/dx= 126*( -1*(x+168)^-2)*(1) > the (1) here is from the chain rule applied to x+168

and your original is now y=42*U^2

so dy/dx = 42*2*U^1*dU/dx >chain rule here thus the dU/dx

sub back in and dy/dx = 84(126/(x+168))*[-126/(x+168)^2)]=-1333584/(x+168)^3

jeez, that's not easy to type....

jerry
 

JohnM

TS Contributor
#4
or you could let:

a = 42
b = 126
c = x + 168

so you start with:
y = a * (b/c)^2

product rule:
y' = [ a * 2(b/c)((cb' - bc')/c^2) ] + [ (b/c)^2 * a' ]

a' and b' are 0, and c' is 1, so they fall out of the equation and we have:
y' = (-2ab^2) / c^3

plug the original values back in:
y' = -1333584 / (x + 168)^3