Subjects calculus

Third Derivative 327D62

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Third Derivative 327D62


1. The third derivative of a function is the derivative of the second derivative. It measures the rate of change of the acceleration of the function. 2. To find the third derivative, start with the original function $f(x)$, then find the first derivative $f'(x)$, the second derivative $f''(x)$, and finally the third derivative $f'''(x)$. 3. The formula for the third derivative is: $$f'''(x) = \frac{d}{dx} \left( f''(x) \right)$$ 4. For example, if $f(x) = x^4$, then: - First derivative: $f'(x) = 4x^3$ - Second derivative: $f''(x) = 12x^2$ - Third derivative: $f'''(x) = 24x$ 5. This process can be applied to any differentiable function to find its third derivative.