Menu Close

If-f-x-sin-4-3x-f-pi-12-




Question Number 150186 by mathdanisur last updated on 10/Aug/21
If   f(x) = sin^4 (3x)  ⇒  f^′ ((π/(12))) = ?
$$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{sin}^{\mathrm{4}} \left(\mathrm{3x}\right)\:\:\Rightarrow\:\:{f}\:^{'} \left(\frac{\pi}{\mathrm{12}}\right)\:=\:? \\ $$
Answered by puissant last updated on 10/Aug/21
f′(x)=4×3cos(3x)sin^3 (3x)  ⇒ f′(x)=12cos(3x)sin^3 (3x)  f′((π/(12)))=12×((√2)/2)×(((√2)/2))^3 =12(((√2)/2))^4 =12((4/(16)))  f′((π/(12)))= 3...
$$\mathrm{f}'\left(\mathrm{x}\right)=\mathrm{4}×\mathrm{3cos}\left(\mathrm{3x}\right)\mathrm{sin}^{\mathrm{3}} \left(\mathrm{3x}\right) \\ $$$$\Rightarrow\:\mathrm{f}'\left(\mathrm{x}\right)=\mathrm{12cos}\left(\mathrm{3x}\right)\mathrm{sin}^{\mathrm{3}} \left(\mathrm{3x}\right) \\ $$$$\mathrm{f}'\left(\frac{\pi}{\mathrm{12}}\right)=\mathrm{12}×\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}×\left(\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\right)^{\mathrm{3}} =\mathrm{12}\left(\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\right)^{\mathrm{4}} =\mathrm{12}\left(\frac{\mathrm{4}}{\mathrm{16}}\right) \\ $$$$\mathrm{f}'\left(\frac{\pi}{\mathrm{12}}\right)=\:\mathrm{3}… \\ $$
Commented by mathdanisur last updated on 10/Aug/21
thank you  Ser
$${thank}\:{you}\:\:{Ser} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *