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Find third derivative

September 22, 2026Mathematics

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To find the third derivative, we start with the given second derivative:

\frac{d^2 y}{dx^2} = -\frac{1}{8}

Differentiate both sides with respect to $x$ to find the third derivative.
$\frac{d}{dx}\left(\frac{d^2 y}{dx^2}\right) = \frac{d}{dx}\left(-\frac{1}{8}\right)$
Since $-\frac{1}{8}$ is a constant, its derivative is zero.
$\frac{d^3 y}{dx^3} = 0$
Answer: The third derivative is 0.

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