KCET · Maths · Complex Number
If \( y=(1+x)\left(1+x^{2}\right)\left(1+x^{4}\right) \), then \( \frac{d y}{d x} \) at \( x=1 \) is
- A \( 28 \)
- B \( 00 \)
- C \( 20 \)
- D \( 11 \)
Answer & Solution
Correct Answer
(A) \( 28 \)
Step-by-step Solution
Detailed explanation
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
\(\left.\frac{d y}{d x}\right|_{x}=1\)
\(=16+4+8=28\)
\(\left.=1+1^{2}\right) 4+(1+1)(1+1)+(1+1)(1+1) 2\)
\(\frac{d y}{d x}=(1+x)\left(1+x^{2}\right) 4 x^{3}+\left(1+x^{2}\right)\left(1+x^{4}\right)+\left(1+x^{4}\right)(1+x) 2 x\)
At \(x=1\), we have
\(\left.\frac{d y}{d x}\right|_{x}=1\)
\(=16+4+8=28\)
\(\left.=1+1^{2}\right) 4+(1+1)(1+1)+(1+1)(1+1) 2\)
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