Subjects calculus

Third Derivative 36F8C3

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Third Derivative 36F8C3


1. Let's find the third derivative of the function from the previous question. First, we need to know the original function $f(x)$. Since it was not provided here, I'll assume it was $f(x) = x^4$ as in the example. 2. The first derivative is found by applying the power rule: $$f'(x) = \frac{d}{dx} x^4 = 4x^3$$ 3. The second derivative is the derivative of the first derivative: $$f''(x) = \frac{d}{dx} 4x^3 = 12x^2$$ 4. The third derivative is the derivative of the second derivative: $$f'''(x) = \frac{d}{dx} 12x^2 = 24x$$ 5. Therefore, the third derivative of $f(x) = x^4$ is $$f'''(x) = 24x$$ If you provide the original function, I can compute the exact third derivative for that function.