[tex]\text{Solution for}[/tex] [tex]f(x)=2x-2[/tex] and [tex]g(x)=5x^2-3[/tex]
[tex] \dfrac{d}{dx} \left(2x-2\right)=2 \ \ \ =\ \textgreater \ \ \ \ \dfrac{d}{dx}\left(2x\right)-\dfrac{d}{dx}\left(2\right)[/tex]
[tex]2\dfrac{d}{dx}\left(x\right) = 2[/tex]
[tex]\dfrac{d}{dx}\left(2\right) = 0[/tex]
[tex]\text{Therefore, 2 - 0 = 2}[/tex]
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[tex]\dfrac{d}{dx}\left(5x^2\right)-\dfrac{d}{dx}\left(3\right)[/tex]
[tex]5\dfrac{d}{dx}\left(x^2\right) =\ \textgreater \ 5 * \:2x =\ \textgreater \ 10x[/tex]
[tex]5*2^2 -3[/tex]
[tex]g(f(2)) = 17 [/tex]
[tex]2*17 -2 = 32
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