Найти производную уравнения y=tgx^3(4x^2). Created by echowahaeski. algebra-ru

Найти производную уравнения y=tgx^3(4x^2)...

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TegeranUA $y=(tgx^{3})(4x^2)
\\y'= (tgx^3)'4x^2+tgx^3(4x^2)'=\frac{3x^2*4x^2}{cos^2x^3}+8xtgx^3=\frac{12x^4}{cos^2x^3}+8x*tgx^3=
\\=4x(\frac{3x^3}{(cosx^3)^2}+2tgx^3)=4x(\frac{3x^3}{(cosx^3)^2}+\frac{2\frac{sinx^3}{cosx^3}*(cosx^3)^2}{(cosx^3)^2})=
\\=4x(\frac{3x^3+2sinx^3cosx^3}{(cosx^3)^2})=4x(\frac{
3x^3+sin2x^3}{(cosx^3)^2})$

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