Another One...

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

If f(x) = e^x² and g(1)=e, the domain of g(x) being (1/2,âˆž), find (a+b) if g(5) = ae^b.

4 Answers

f'g+fg'=f'g'

e^x²g'+e^x²x²2x g =e^x²x²2x g'

e^x²x²2x g =e^x²(x²2x-1) g'

x²2x g =(x²2x-1) g'

g'/g = (2x³-1)/2x³ = 1-x^-3/2

Now solve...

Bhaiyaa, d/dx(e^x²) = e^x².2x 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.e^1/2 => K = e^1/2 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]

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

i am the new jughead :P

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