This is a straight forward question..
When I have something like 10/x (i.e basically whenever the numerator is just a number with no variables) and I need to take the derivative I go through the whole quotient process knowing first off the 10 will disappear, really meaning my numerator will start with – .
I go – 10 * derivative of denominator all divided by denominator ^2.
Typically I write it out completely and it feels like maybe I'm making it into some thing that could be done a lot shorter.
Is there a short cut people employ with these straight forward derivatives e.g 50/x, 10/2y ..basically whenever the numerator is just a number with no variables
Best Answer
If you ever see $$f(x)=\frac{10}{x}$$ just write $$f(x)=10 \cdot x^{-1}$$ and differentiate using the power rule.
You would use the quotient rule to differentiate a fraction composed of a numerator with more than 2 terms of the independent variable.
If you did use the quotient rule to differentiate $$f(x)=\frac{10}{x}$$ we would get:
$$f'(x)= \frac {10 \cdot \frac{d(10)}{dx} \cdot x - \frac{d(x)}{dx}\cdot 10}{x^2} \implies \frac{-10}{x^2}$$