Question

Производная (похідна)

Answer 1

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