Question

Помогите с производными:
1. y=tg(3x+7)*lg(6x+3)
2. y = tg(x)^5+(tg(6x-7)/lgx)

Answer 1

Производная произведения
$(f*g)' = f'*g + f*g'$

$y'=(tg(3x+7)*lg(6x+3))' = \ \ = (tg(3x+7))'*lg(6x+3) + tg(3x+7)*(lg(6x+3))' = \ \ = frac{3}{cos^2 (3x+7)} *lg(6x+3) + tg(3x+7) * frac{6}{(6x+3)ln10}$

Производная суммы и частного
$( frac{f}{g})' = frac{f'*g - f*g'}{g^2}$

$y' = (tg^5x+ frac{tg(6x-7)}{lgx} )' = 5tg^4x* frac{1}{cos^2x} + frac{(tg(6x-7))'*lgx+tg(6x-7)*(lgx)'}{lg^2x} = \ \ = 5tg^4x* frac{1}{cos^2x} + frac{ frac{6}{cos^2(6x-7)}lgx -tg(6x-7)* frac{1}{xln10} }{lg^2x}$