Question

find the nth derivative log(x+5x+6)​

Answer 1

Answer:

1) When n is even:

(-1)*(n-1)!/[{x+1}^n]

2) When n is odd:

(n-1)!/[{x+1}^n]

Explained:

y=log(x+5x+6)

y=log(6x+6)

Now taking out the first derivative,

y'=6/(6x+6)

y'=1/(x+1)

Second derivative,

y''=(-1)*(1)/[(x+1)^2]

Third derivative,

y'''=(1)*(2)/[(x+1)^3]

Fourth derivative,

y''''=(-1)*(2)*(3)/[(x+1)^4]

Following the above sequence,

nth derivative of y will be:

1) When n is even: (-1)*(n-1)!/[{x+1}^n]

2) When n is odd:

(n-1)!/[{x+1}^n]