# Calculus

f(x)=(x-α)(x-β).... prove derivative of f(x)/f(x) = 1/x-α+1/x-β....

Note by Hrushikesh Behera
1 year, 2 months ago

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$$f(x)=(x-\alpha)(x-\beta)$$

$$\log(|f(x)|)=\log(|x-\alpha|)+\log(|x-\beta|)$$

$$\text{Differentiating,we get,}$$

$$\dfrac{f'(x)}{f(x)}=\dfrac{1}{(x-\alpha)}+\dfrac{1}{(x-\beta)}$$

- 1 year, 2 months ago