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### Give the function whose nth derivative is equal to function itself ...? ____________________________________

```     x
e
```
##### Explanation
```                           x            x
We know the derivative of e   is again e  (i.e itself)
x     x
First derivative of e  = e
x    x
Second derivative of e  = e
.
.
.
x    x
nth derivative of e  = e
```

Therefore e^x is the function whose derivative of any order (first, second, third, …nth derivative) is equal to the function itself.
Now let see 2nd option e^-x. Its first derivate is -e^-x, 2nd derivative is e^-x, 3rd derivative is -e^-x, ...
Now let see 3rd option e^f(x). Its first derivate is e^f(x) . f'(x) and 2nd derivative is e^f(x) . f''(x), ...

Therefore e^x is the only function whose nth derivative is equal to the function itself.

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##### SHORTCUT TRICKS (Division)
• Divisible by 2 Shortcut trick
• Divisible by 3 Shortcut trick
• Divisible by 4 Shortcut trick
• Divisible by 5 Shortcut trick
• Divisible by 6 Shortcut trick • Divisible by 7 Shortcut trick • Divisible by 8 Shortcut trick • Divisible by 9 Shortcut trick
• Divisible by 10 Shortcut trick

##### Worksheets (Solved)

###### Integration     