Question

prove the following product rules formula by writing thing out term coordinates (f(t)r(t))`=f`(t)r(t)+f(t)r`(t)

Answer 1

Using chain rule
\[ \frac{d}{dx} (f(x)g(x)) = \frac{d}{df}(f(x)g(x))\times \frac{d}{dx}f(x) + \frac{d}{dg}(f(x)g(x))\times \frac{d}{dx}g(x) \\
\\
\space =g(x)f'(x) + g'(x) f(x)
\]

Answer 2

where f in denominator stands for f(x) and g for g(x)