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Question

The derivative of 7x24ex−x will be

A
7(8ex4xexx)(4exx)2
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B
7x(8ex4xexx)(4exx)2
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C
7x(8ex4xex1)(4exx)2
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D
None of these
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Solution

The correct option is B 7x(8ex4xexx)(4exx)2
It’s easy to figure out that the function is quotient of two functions 7x2 and 4exx. So we will use the quotient rule which says

ddx(f(x)g(x))=f(x)×g(x)g(x)×f(x)(g(x))2

f(x) here is 7x2, f(x)=14x
g(x) here is 4exx, g(x) will be 4ex1
Just substitute the terms in the formula and the derivative will be
(4exx)(f(x))7x2×g(x)(g(x))2=(4exx)×(14x)(7x2)×(4ex1)(4exx)2

=56xex14x214x2(28x2ex7x2)(4exx)2

=56xex14x228x2ex+7x2(4exx)2

=7x(8ex4xexx)(4exx)2.

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