Q110 / 180 · KCET 2014 · Mathematics

If \( y=(1+x)\left(1+x^{2}\right)\left(1+x^{4}\right) \), then \( \frac{d y}{d x} \) at \( x=1 \) is

  • Correct answer
    A
    \( 28 \)
  • B
    \( 00 \)
  • C
    \( 20 \)
  • D
    \( 11 \)

Solution

Given that, $y=(1+x)\left(1+x^{2}\right)\left(1+x^{4}\right)$ $\frac{d y}{d x}=(1+x)\left(1+x^{2}\right) 4 x^{3}+\left(1+x^{2}\right)\left(1+x^{4}\right)+\left(1+x^{4}\right)(1+x) 2 x$ At $x=1$, we have $\left.\frac{d y}{d x}\right|_{x}=1$ $=16+4+8=28$ $\left.=1+1^{2}\right) 4+(1+1)(1+1)+(1+1)(1+1) 2$

Hence, the correct answer is option: 'A'.

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