Question

Solve
$y=(1+x)(1+x^2)(1+x^4),then\frac{dy}{dx}atx=0is$

• A. 1
• B. -1
• C. 0
• D. 2

Answer 1

Answer: (A)

1

Given $y=(1+x)(1+x^2)(1+x^4)$

At $x=0,y=(1+0)(1+0)(1+0)=1$

$y=(1+x)(1+x^2)(1+x^4)$

$⟹\log y=\log (1+x)+\log (1+x^2)+\log (1+x^4)$

Differentiating on both sides

$⟹\frac{1}{y}\frac{dy}{dx}=\frac{1}{1+x}+\frac{2x}{1+x^2}+\frac{4x^3}{1+x^4}$

At $x=0,\frac{1}{1}\times \frac{dy}{dx}=\frac{1}{1+0}+\frac{0}{1+0}+\frac{0}{1+0}=1⟹\frac{dy}{dx}=1$