Question Number 123706 by I want to learn more last updated on 27/Nov/20
![If h(x) = f^2 (x) − g^2 (x), f ′(x) = − g(x) and g ′(x) = f(x) then h ′(x) = ??? (a) 0 (b) 1 (c) − 4 f(x) g(x) (d) [−g(x)]^2 − [f(x)]^2](https://www.tinkutara.com/question/Q123706.png)
$$\mathrm{If}\:\:\:\:\mathrm{h}\left(\mathrm{x}\right)\:\:=\:\:\mathrm{f}^{\mathrm{2}} \left(\mathrm{x}\right)\:\:−\:\:\mathrm{g}^{\mathrm{2}} \left(\mathrm{x}\right),\:\:\:\:\:\:\:\:\mathrm{f}\:'\left(\mathrm{x}\right)\:\:\:=\:\:\:−\:\mathrm{g}\left(\mathrm{x}\right)\:\:\:\:\mathrm{and}\:\:\:\:\:\mathrm{g}\:'\left(\mathrm{x}\right)\:\:=\:\:\mathrm{f}\left(\mathrm{x}\right) \\ $$$$\:\:\:\mathrm{then}\:\:\:\:\mathrm{h}\:'\left(\mathrm{x}\right)\:\:=\:\:\:??? \\ $$$$ \\ $$$$\left(\mathrm{a}\right)\:\:\:\:\mathrm{0}\:\:\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{c}\right)\:\:\:\:\:−\:\:\mathrm{4}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{g}\left(\mathrm{x}\right)\:\:\:\:\:\:\:\:\:\:\left(\mathrm{d}\right)\:\:\:\:\:\left[−\mathrm{g}\left(\mathrm{x}\right)\right]^{\mathrm{2}} \:\:−\:\:\left[\mathrm{f}\left(\mathrm{x}\right)\right]^{\mathrm{2}} \\ $$
Answered by Bird last updated on 27/Nov/20
$${h}^{'} \left({x}\right)=\mathrm{2}{f}\left({x}\right){f}^{'} \left({x}\right)−\mathrm{2}{g}\left({x}\right){g}^{'} \left({x}\right) \\ $$