Find the derivative of the function.
1. 2x+5/3x-2
2. (1-x)(1+x^2)^-1
Please show work. TYVM. :)
Use the quotient rule (gf’-fg’)/g^2 where f is the numerator and g is the denominator.
For number 1 f=2x+5 so f’ is 2 and g is 3x-2 so g’ is 3
The derivative is ((3x-2)2-(2x+5)3)/(3x-2)^2
After simplifying the final answer is –19/(3x-2)^2
For number 2 rewrite it as (1-x)/(1+x^2)
f=1-x f’=-1 g=1+x^2 g’=2x
((1+x^2)(-1)-(1-x)(2x))/(1+x^2)^2
Simplify -1+x^2-2x/(1+x^2)^2