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`e^(x//2)``e^(x)``e^(2x)``e^(4x)`

Solution :

`"Given "f=f'+f''+f'''+...oo` <br> `"or "f'=f''+f'''+f'''+...oo` <br> `"or "f-f'=f'` <br> `"or "f=2f'` <br> `"Hence, "(f')/(f)=1//2 or int(f')/(f)dx=int(1)/(2)dx` <br> `"or "logf(x)=x//2+c` <br> `"or "f(x)=e^(x//2+c)` <br> `"Also, "f(0)=1 or c = 0 or f(x) =e^(x//2)`**Definition and geometric meaning.**

**Differentiation by first principle: sin x**

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**Differentiation Of Implicit Functions**

**Find differentiation of `arc sinx` using first principle**

**Find differentiation of `arc cosx` using first principle**

**Derivation of all well known results**

**Diffrentiate ` e^(2x)` and `e^sinx`**