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Question

What is dydx if y=(x1)2(x+2)3


A

y[x12+x+23]

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B

y.[2(x1)+3(x+2)]

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C

2x1+x+23

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D

y[2x1+3x+2]

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Solution

The correct option is D

y[2x1+3x+2]


Given that,

y=(x1)2(x+2)3

We need to use logarithmic differentiation since the function is a product of 2 factors and involves powers.

Upon taking logarithm this changes into addition and multiplication respectively.

lny = 2.ln(x-1)+3.ln(x+2)

Differentiating both sides.

1y.y=2(x1)+3x+2 (Chain rule is applied on the LHS)

y=y[2x1+3x+2]

Hence answer is option (d).


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