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Question Number 123706 by I want to learn more last updated on 27/Nov/20

$$\mathrm{If}\mathrm{h}\left(\mathrm{x}\right)={\mathrm{f}}^2\left(\mathrm{x}\right)-{\mathrm{g}}^2\left(\mathrm{x}\right),\mathrm{f}{}^{\prime }\left(\mathrm{x}\right)=-\mathrm{g}\left(\mathrm{x}\right)\mathrm{and}\mathrm{g}{}^{\prime }\left(\mathrm{x}\right)=\mathrm{f}\left(\mathrm{x}\right)$$$$\mathrm{then}\mathrm{h}{}^{\prime }\left(\mathrm{x}\right)=???$$$$$$$$\left(\mathrm{a}\right)0\left(\mathrm{b}\right)1\left(\mathrm{c}\right)-4\mathrm{f}\left(\mathrm{x}\right)\mathrm{g}\left(\mathrm{x}\right)\left(\mathrm{d}\right){[-\mathrm{g}\left(\mathrm{x}\right)]}^2-{\left[\mathrm{f}\left(\mathrm{x}\right)\right]}^2$$

Answered by Bird last updated on 27/Nov/20

$$h^{{}^{\prime }}\left(x\right)=2f\left(x\right)f^{{}^{\prime }}\left(x\right)-2g\left(x\right)g^{{}^{\prime }}\left(x\right)$$

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