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Question

If g(x) = 2f(x) + x + log (f(x)) then d(g(x))d(f(x))_________

A
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B
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C
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D
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Solution

The correct option is B
We discussed in the videos that if y=f(x) and z=ϕ(x)
then dydx=f(x)ϕ(X)
Same thing we will apply here
d(g(x))d(f(x))=g(x)f(x)g(x)=2f(x)+x+log(f(x))g(x)=2f(x)+1+1f(x)x f(x)
So g(x)f(x)will be2f(x)+1+f(x)f(x)f(x)=2+1f(x)+1f(x) (Note that Chain rule is applied here for log(f(x))
which is the correct answer.

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