Q106 / 160 · TS EAMCET 2024 (09 May Shift 2) · Mathematics

If $y=44 x^{45}+45 x^{-44}$, then $y^{\prime \prime}=$

  • Correct answer
    A
    $\frac{1980 y}{x^2}$
  • B
    $\frac{2020 x^2}{y}$
  • C
    $\frac{2024 y}{x^2}$
  • D
    $\frac{1990 x^2}{y}$

Solution

$y=44 x^{45}+45 x^{-44} \Rightarrow y^{\prime}=44 \times 45\left(x^{44}-x^{-45}\right)$ $\begin{aligned} & y^{\prime \prime}=44 \times 45\left(44 x^{43}+45 x^{-46}\right) \\ & =1980 \frac{\left(44 x^{45}+45 x^{-44}\right)}{x^2} \therefore y^{\prime \prime}=\frac{1980 y}{x^2} .\end{aligned}$

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

Relevant Questions