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Q)

If $ y = 5 \cos x - 3 \sin x $ , what is $\large\frac{d^2y}{dx^2} $

$\begin{array}{1 1} -y \\ y^2 \\ y \\1+y \end{array} $

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A)
Toolbox:
  • $y=f(x)$
  • $\large\frac{dy}{dx}$$=f'(x)$
  • $\large\frac{d^2y}{dx^2}=\frac{d}{dx}\big(\frac{dy}{dx}\big)$
  • $\large\frac{d}{dx}$$(\sin x)=\cos x$
  • $\large\frac{d}{dx}$$(\cos x)=-\sin x$
Step 1:
$y=5\cos x-3\sin x$
Differentiating with respect to $x$
$\large\frac{dy}{dx}$$=-5\sin x-3\cos x$
Step 2:
$\large\frac{d^2y}{dx^2}$$=-5\cos x+3\sin x$
$\quad\;=-(5\cos x-3\sin x)$
$\quad\;=-y$
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