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If F(x) = \int f(x)\;dx and G(x) = \int g(x)\;dx, then evaluate \frac{d}{dx}(F(x)\cdot G(x))

  • Option 1)

    f\cdot g

  • Option 2)

    Ff + Gg

  • Option 3)

    Fg + Gf

  • Option 4)

    f + g

 

Answers (1)

best_answer

As we have learnt,

 

Indefinite integration -

It is inverse process of differentation.

\frac{d}{dx}\left \{ F(x) \right \}= f(x)

\therefore \int f(x)dx= F\left ( x \right )+C

 

- wherein

Where

\frac{d}{dx}F\left ( x \right ) is differential of F(x) w.r.t  x

 

 \frac{\mathrm{d} }{\mathrm{d} x}(F(x)G(x)) = F(x)G'(x) + F'(x)G(x) \\* \Rightarrow \frac{\mathrm{d} }{\mathrm{d} x}(F(x)G(x)) = F(x)g(x) + G(x)f(x)

 


Option 1)

f\cdot g

Option 2)

Ff + Gg

Option 3)

Fg + Gf

Option 4)

f + g

Posted by

prateek

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