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6Solution :

`f(x+y)=f(x)f(y)" (1)"` <br> `f'(5)=underset(hrarr0)lim(f(5+h)-f(5))/(h)` <br> `=underset(hrarr0)lim(f(5)f(h)-f(5))/(h)` <br> `=f(5)underset(hrarr0)lim(f(h)-1)/(h)` <br> `=f(5)underset(hrarr0)lim(f(h)-1)/(h)` <br> In (1), replace x by 5 and y by 0. Then, `f(5+0)=f(5)cdotf(0)` <br> `"or "f(0)=1` <br> `"or "f'(5)=f(5)underset(hrarr0)lim(f(h)-f(0))/(h)` <br> `=f(5)f'(0)=2xx3=6`Transcript

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00:00 - 00:59 | hello friends so here is a question in which we have been provided with this condition and we also know that upon 5 is equal to 2 and a dash of zero is equal to 3 and we have to find the value of f dash 5 so to start with I am using the decent which we all know that f dash x is equal to Limit X tends to zero f of X + H - fx4 / h ok ok we have diskpart and according to a condition we can write f of X + Aaj as F of X into a page using this condition it will become f dash x-equis to Limit X tends to zero f of X into f of h mai |

01:00 - 01:59 | FX old / h no in this equation I'm putting x is equal to 5 again it will become f dash 5 equals to Limit X tends to zero ff5 into f h - F5 old / h ok now taking a five common it will become a 5 into limit X tends to zero as a h minus 1 whole divided by using a given condition that is f of X + Y is equal to effect in to avoid putting it is equal to 5 and Y = 20 in this condition ok if it will become f x + Y is equals to F of X in to Fir ok this was the given |

02:00 - 02:59 | u i am putting x is equal to 5 and Y = 20 ok it will become F5 plus 0 = 25 into a 40 ok so from here will become a fan of 5 = 25 into a 10 cancelling A5 it will become even have it at 101 ok so from here we get that the value of a 40 is basically 1 no I am using this thing in any question number 1 distinct and equation 1 if you become test 5 is equal to F5 limit X tends to zero h - no in the place of one I am putting a 40 ke can write one as a 40 it so I am reading |

03:00 - 03:59 | 0h ok so it is limit X tends to zero FL 20 se 40 / not this whole thing will become attached 0 we all know that Avdesh x x x 20 f of X + X - exhibited bache ok here if you put x is equal to zero it will become f h - 40 age and the same thing we have here so basically this thing is equal to dash zero so this will become f dash 5 is equal to F5 in 2-0 in a question we have been provided the value of a 5 is basically equal to 2 and evaluation of dash zero is equal to 3 so from here with god that the value of f dash 5 will be equal to |

04:00 - 04:59 | sex and that is answer it is so I hope this will help you thank you so much |