How to solve
For a quotient u/v, the derivative is (u'v − uv')/v². The minus sign matters: it is not symmetric in u and v. These drills use linear numerator and denominator so the algebra stays manageable after simplifying.
Steps
- Identify u and v; compute u' and v'.
- Form (u'v − uv')/v².
- Simplify the numerator carefully; leave the answer in a compact form.
Example
Differentiate (2x + 1)/(x − 1).
- u = 2x + 1, u' = 2; v = x − 1, v' = 1.
- Numerator: 2(x − 1) − (2x + 1)(1) = 2x − 2 − 2x − 1 = −3.
- Derivative: −3/(x − 1)².
Answer: -3/(x-1)^2
How to type answers
- Enter simplified like 2/(x+1)^2 or -3/(2x-1)^2
Loading drills…