Find Nth Derivative Of `a^(mx)` || YouTube

Nth Derivative Of a^(mx)

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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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