Another One...

Functions f(x) & g(x) are such that - (f.g)'= (f'.g').

If f(x) = ex2 and g(1)=e, the domain of g(x) being (1/2,∞), find (a+b) if g(5) = aeb.

4 Answers

62
Lokesh Verma ·

f'g+fg'=f'g'

ex2g'+ex2x22x g =ex2x22x g'

ex2x22x g =ex2(x22x-1) g'

x22x g =(x22x-1) g'

g'/g = (2x3-1)/2x3 = 1-x-3/2

Now solve...

13
Avik ·

Bhaiyaa, d/dx(ex2) = ex2.2x only naa ?? [186]

I got, g'/g = 2x/(2x-1)

Sloving which, am getting smthing like-
g(x)=K.e^{\frac{2x-1}{2} +\frac{ln(2x-1)}{2}

& On substituting x=1, e = K.e1/2 => K = e1/2 Which results in...

g(x)=e^{\frac{2x-1}{2} +\frac{ln(2x-1)}{2}+\frac{1}{2}

Using this, i get 6,

But, the answer is 8......Where am i going wrong?? [2]

13
Avik ·

Okie got it....! was making a silly mistake...thnx bhaiyaa...

62
Lokesh Verma ·

i am the new jughead :P

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