Asked by Matthew
Find the derivative of the function.
1. 2x+5/3x-2
2. (1-x)(1+x^2)^-1
Please show work. TYVM. :)
1. 2x+5/3x-2
2. (1-x)(1+x^2)^-1
Please show work. TYVM. :)
Answers
Answered by
johnathon
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
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
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.