Question

Производная (похідна)

Answer 1

$y'=[sqrt{5x^2+12x-4*log_4(cos(x))}]'=\\ =frac{1}{2*sqrt{5x^2+12x-4*log_4(cos(x))}}*[5x^2+12x-4*log_4(cos(x))}]'=\\ =frac{[5x^2]+[12x]'-[4*log_4(cos(x))]'}{2*sqrt{5x^2+12x-4*log_4(cos(x))}}}\\ =frac{10x+12-4*frac{1}{cos(x)*ln(4)}*[cos(x)]'}{2*sqrt{5x^2+12x-4*log_4(cos(x))}}}=\\ =frac{10x+12+frac{4*sin(x)}{cos(x)*ln(4)}}{2*sqrt{5x^2+12x-4*log_4(cos(x))}}}$