Question

find the nth derivative of (i) 1 /(x+2) (x+3)​

Answer 1

Answer:

ddx(3−2x)−3=(−3)(−2)(3−2x)−4

ddx(−3)(−2)(3−2x)−4=(−3)(−4)(−2)2(3−2x)−5

Each derivative would be having positive coefficients because the power is negative and the coefficient of x inside the bracket is also negative. So we don't have to care about the sign.

You can expect that

dndxn(3−2x)−3=2n(3×4×⋯×(3+n−1))(3−2x)−3−n=2n−1(n+2)!(3−2x)n+3