Nth Derivative Of Log(ax+b) | Successive Derivatives Solved Examples

Nth Derivative Of Log(ax+b) 

in this quick tutorial we will learn how to find nth derivative of a logarithmic function like " Log( ax+b )" by successive differentiation method. So observe each and every step very carefully. 

 Given            y = log(ax+b)

Sol: Differentiating ‘y’ with respect to ‘x’ we get

`y_1` = `\frac{1}{(ax + b)}`             or  `y_1`  = a. `(ax + b)^{ - 1}`

Now differentiating `{y_1}` again we get:

`y_2` = (-1). `a^{2}` .  `(ax + b)^{ - 2}`

Differentiating `y_2` again w.r.t x we get 

`y_3` = (-1). (-2). `a^{ 3}`  `(ax + b)^{ - 3}`

again differentiating `y_3` again w.r.t x we get 

`y_4` = (-1). (-2). (-3) `a^{ 4}`  `(ax + b)^{ - 4}`

Now differentiating `y` w.r.t x successively until we find `n_th` derivative of `y`

---------------------------------------------

----------------------------------------

--------------------------------------------

Finally we achieve `n_th` derivative of `y` 

which is: 

`y_n` = (-1). (-2). (-3)........................ upto (n-1) `a^{n}`  `(ax + b)^{ - n}`

or `n_th` derivative of `y`

`y_n` = `\frac{(n - 1)!. a^n}{(ax + b)^{ - n}}`

_________________________________________

            Watch video solution here 👇

_________________________________________