Question

What is $\frac{dy}{dx}ify=(x-1{)}^2(x+2{)}^3$

• A. $y[\frac{x-1}{2}+\frac{x+2}{3}]$
• B. $y.\left[2\right(x-1)+3(x+2\left)\right]$
• C. $\frac{2}{x-1}+\frac{x+2}{3}$
• D. $y[\frac{2}{x-1}+\frac{3}{x+2}]$

Answer 1

The correct option is D

$y[\frac{2}{x-1}+\frac{3}{x+2}]$

Given that,

$y=(x–1{)}^2(x+2{)}^3$

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.

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

Differentiating both sides.

$\frac{1}{y}.y^{\prime }=\frac{2}{(x-1)}+\frac{3}{x+2}$ (Chain rule is applied on the LHS)

$y^{\prime }=y[\frac{2}{x-1}+\frac{3}{x+2}]$

Hence answer is option (d).