Question

determine a derivada
f(x)=cossec ( 2x³-4x²+2)

Answer 1

$f\left(x \right )=\mathrm{cossec}\left(2x^{3}-4x^{2}+2 \right )\\ \\ \\ f'\left(x \right )=\left[\,\mathrm{cossec}\left(2x^{3}-4x^{2}+2 \right )\, \right ]'\\ \\ f'\left(x \right )=-\mathrm{cotg}\left(2x^{3}-4x^{2}+2 \right )\cdot \mathrm{cossec}\left(2x^{3}-4x^{2}+2 \right )\cdot \left(2x^{3}-4x^{2}+2 \right )'\\ \\ f'\left(x \right )=-\mathrm{cotg}\left(2x^{3}-4x^{2}+2 \right )\cdot \mathrm{cossec}\left(2x^{3}-4x^{2}+2 \right )\cdot \left(6x^{2}-8x \right )$