Nth Derivative Of a^(mx)

In this quick math tutorial you will learn how to find the Nth Derivative of a^(mx) by successive differentiation method. So please observe each step very carefully.

To Find `N_th` derivative of `a^(mx)`

Let `y` = `a^(mx)`

Differentiating `y` w.r.t `x` we get …..

`y_1` = m. `a^(mx)`. `log a`

Now Differentiating `y_1` w.r.t `x` we get………..

`y_2` = `m^(2)`. `a^(mx)`. `(log a)^(2)`

Again Differentiating `y_2` w.r.t `x` we get………..

`y_3` = `m^(3)`. `a^(mx)`. `(log a)^(3)`

Again Differentiating `y_3` w.r.t `x` we get………..

`y_4` = `m^(4)`. `a^(mx)`. `(log a)^(4)`

Now we keep differentiating `y` successively until we reach `n_th` derivative

So, `y_5` = ……………………….

And `y_6` = ………………………..

…………………………………….

Finally, `y_n` = `m^(n)`. `a^(mx)`. `(log a)^(n)`

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😊 let's understand this with the help of this video tutorial 😊

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