What is dydx if y=(x−1)2(x+2)3
y[2x−1+3x+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.
∴ lny = 2.ln(x-1)+3.ln(x+2)
Differentiating both sides.
1y.y′=2(x−1)+3x+2 (Chain rule is applied on the LHS)
y′=y[2x−1+3x+2]
Hence answer is option (d).