Question Number 228430 by Kassista last updated on 13/Apr/26
Answered by TonyCWX last updated on 16/Apr/26
![det(g(x)) = 64sin(x)ln(x)− 2^(cos(x) + 3) [48(x^2 − 3x + 5)] M_g (x) = 64cos(x)ln(x) + ((64sin(x))/x) − ln(2)[−sin(x)]2^(cos(x) + 3) [48(x^2 − 3x + 5)] − 2^(cos(x) + 3) [48(2x − 3)] M_g (5) = 64cos(5)ln(5) + ((64sin(5))/5) + ln(2)[sin(5)]2^(cos(5) + 3) [48(5^2 − 3(5) + 5)] − 2^(cos(5) + 3) [48(2(5) − 3)] M_g (5) = 64cos(5)ln(5) + ((64sin(5))/5) + 720ln(2)[sin(5)]2^(cos(5) + 3) − (336)2^(cos(5) + 3)](https://www.tinkutara.com/question/Q228457.png)
$$\mathrm{det}\left({g}\left({x}\right)\right)\:=\:\mathrm{64sin}\left({x}\right)\mathrm{ln}\left({x}\right)−\:\mathrm{2}^{\mathrm{cos}\left({x}\right)\:+\:\mathrm{3}} \left[\mathrm{48}\left({x}^{\mathrm{2}} \:−\:\mathrm{3}{x}\:+\:\mathrm{5}\right)\right] \\ $$$${M}_{{g}} \left({x}\right)\:=\:\mathrm{64cos}\left({x}\right)\mathrm{ln}\left({x}\right)\:+\:\frac{\mathrm{64sin}\left({x}\right)}{{x}}\:−\:\mathrm{ln}\left(\mathrm{2}\right)\left[−\mathrm{sin}\left({x}\right)\right]\mathrm{2}^{\mathrm{cos}\left({x}\right)\:+\:\mathrm{3}} \left[\mathrm{48}\left({x}^{\mathrm{2}} \:−\:\mathrm{3}{x}\:+\:\mathrm{5}\right)\right]\:−\:\mathrm{2}^{\mathrm{cos}\left({x}\right)\:+\:\mathrm{3}} \left[\mathrm{48}\left(\mathrm{2}{x}\:−\:\mathrm{3}\right)\right] \\ $$$${M}_{{g}} \left(\mathrm{5}\right)\:=\:\mathrm{64cos}\left(\mathrm{5}\right)\mathrm{ln}\left(\mathrm{5}\right)\:+\:\frac{\mathrm{64sin}\left(\mathrm{5}\right)}{\mathrm{5}}\:+\:\mathrm{ln}\left(\mathrm{2}\right)\left[\mathrm{sin}\left(\mathrm{5}\right)\right]\mathrm{2}^{\mathrm{cos}\left(\mathrm{5}\right)\:+\:\mathrm{3}} \left[\mathrm{48}\left(\mathrm{5}^{\mathrm{2}} \:−\:\mathrm{3}\left(\mathrm{5}\right)\:+\:\mathrm{5}\right)\right]\:−\:\mathrm{2}^{\mathrm{cos}\left(\mathrm{5}\right)\:+\:\mathrm{3}} \left[\mathrm{48}\left(\mathrm{2}\left(\mathrm{5}\right)\:−\:\mathrm{3}\right)\right] \\ $$$${M}_{{g}} \left(\mathrm{5}\right)\:=\:\mathrm{64cos}\left(\mathrm{5}\right)\mathrm{ln}\left(\mathrm{5}\right)\:+\:\frac{\mathrm{64sin}\left(\mathrm{5}\right)}{\mathrm{5}}\:+\:\mathrm{720ln}\left(\mathrm{2}\right)\left[\mathrm{sin}\left(\mathrm{5}\right)\right]\mathrm{2}^{\mathrm{cos}\left(\mathrm{5}\right)\:+\:\mathrm{3}} \:−\:\left(\mathrm{336}\right)\mathrm{2}^{\mathrm{cos}\left(\mathrm{5}\right)\:+\:\mathrm{3}} \\ $$
Commented by Kassista last updated on 17/Apr/26
$${thanks}!! \\ $$