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Question

The derivative of (x3+ln6)(x) will be

A
32x3/2
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B
3x2x
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C
3x2x+x3+ln62x
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D
None of the above
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Solution

The correct option is C 3x2x+x3+ln62x
If we closely watch the given function, it is the product of two different functions i.e., (x3+ln6) and x. So don't you think that we can solve this by applying product rule for derivatives? The rule says that,
dd(x)[f(x)×g(x)]=dd(x)(f(x))×g(x))+ddx(g(x))×f(x))So, dd(x)[(x3+ln6)(x)]=dd(x)(x3+ln6)×(x)+dd(x)(x)×(x3+ln6)=(3x2+0)(x)+(x3+ln6)(12x1/2)=3x2x+x3+ln62x
Which is the option C.
By the way this question can also be solved using addition rule for differentiation if you write the above function as,
x2x+ln6x
i.e. x5/2+ln6x

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