Applied Calculus
posted by Jacob on .
Find the first and second derivative of the function:
x/(7x+10)
Using quotient rule. This is part of my homework in the section named "Higher Order Derivatives". I am confused on getting the second derivative, as I found the first derivative to be 10/(7x+10)^2

I agree with your first derivative.
Now, start with 10/(7x+10)^2 and take the derivative again.
Denom times deriv of numerator = 0
since deriv of 10 = 0
minus the numer time the deriv of the denomin.
 10(2(7x+10)7) this is the chain rule
You need to simplify this expression
all over the denominator squared which makes the denominator to the 4th power. 
y=x/(7x+10)
y'=1/( )  7x/( )^2
= (7x+10)x  7x)/ (7x+10)^2
and that is not equal to your answer.
= (7x^2 +3x)/(7x+10)^2