Question

How do I find the derivative of y= (fg)/h in terms of f, g, h, h, f', g' and h' where f, g, and h are functions of x?

Answer 1

\[y= \frac{ fg }{ h }\] This is what if looks like.

Answer 2

\[y=\frac{fg}{h}\]
\[\begin{align*}\frac{dy}{dx}&=\frac{h\dfrac{d}{dx}[fg]-(fg)\dfrac{d}{dx}[h]}{h^2}&&\text{quotient rule}\\
&=\frac{h\left(f\dfrac{d}{dx}[g]+g\dfrac{d}{dx}[f]\right)-f~g~h'}{h^2}&&\text{product rule for }fg\\
&=\frac{h\left(f~g'+g ~f'\right)-f~g~h'}{h^2}\\
&=\frac{f'~g~h+f~g'~h-f~g~h'}{h^2}
\end{align*}\]

Answer 3

Thank you so much.

Answer 4

you're welcome