Question

Найдите производную функции

y=4√2x³+8


y=tg²x/2

Answer 1

$y_1=4 sqrt{2x^3+8} \y'= frac{4}{2 sqrt{2x^3+8} } *(2x^3+8)'\y'=frac{12x^2}{ sqrt{2x^3+8} } \y=frac{tg^2(x)}{2} \y'=frac{(tg^2(x))'*2-tg^2(x)(2)'}{4} \y'=frac{(tg^2(x))'*2}{4} \y=tg^2(x)\y'=2tg(x)*tg^{'}(x)\\ y'=frac{2tg(x)}{cos^2(x)} \y'=(frac{2tg(x)}{cos^2(x)} ):2\y'=frac{tg(x)}{cos^2(x)}$