Question

find the second derivative of x^3-5x^2+x=0​

Answer 1

Answer :-

First derivative of x³ - 5x² + x = 0 :-

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Using power rule and sum rule -

• $\sf Power \:rule - \dfrac{d}{dx}x^n = nx^{n-1}$

• $\sf Sum \:rule - \dfrac{d}{dx}(u \pm v) = \dfrac{du}{dx} \pm \dfrac{dv}{dx}$

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$\implies\sf\dfrac{d}{dx}(x^3 - 5x^2 + x)$

$\implies\sf\dfrac{d(x^3)}{dx} - \dfrac{d(5x^2)}{dx} + \dfrac{d(x)}{dx}$

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• $\sf \dfrac{d(x^3)}{dx} = 3x^2$

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• $\sf \dfrac{d(5x^2)}{dx} = 10x$

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• $\sf \dfrac{d(x)}{dx} = 1$

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$\implies\sf3x^2 - 10x + 1$

Second derivative of x³ - 5x² + x = 0 :-

$\implies\sf\dfrac{d}{dx}(3x^2-10x+1)$

$\implies\sf\dfrac{d(3x^2)}{dx} - \dfrac{d(10x)}{dx} +\dfrac{d(1)}{dx}$

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• $\sf \dfrac{d(3x^2)}{dx} = 6x$

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• $\sf \dfrac{d(10x)}{dx} = 10$

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• $\sf \dfrac{d(1)}{dx} = 0$

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$\implies\boxed{\sf 6x - 10}$

Answer 2

1. The second derivative is equal to 6x – 10