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Find the differential $dy$ and evaluate $dy$ for the given values of $x$ and $dx$\[\]$y=(x^{2}+5)^{3},x=1,dx=0.1$

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1 Answer

  • Let $y=f(x)$ be a differentiable function then the quantities $dx$ and $dy$ are called differentials.The differential $dx$ is an independent variable.
  • The differential $dy$ is then defined by $dy=f'(x)dx(dx \approx \Delta x)$
  • Also $f(x+\Delta x)-f(x)=\Delta y =dy $ from which $f(x+\Delta x) $can be evaluated
Step 1:
Step 2:
When $x=1,dx=0.05$
$dy= 6(6)^2(0.05)$
$\quad=216 (0.05)$
answered Aug 12, 2013 by meena.p

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