Question

f(x)=sinx/(3cos^2*x) помогите найти производную

Answer 1

$f(x)=\frac{sinx}{3cos^2x}=\frac{1}{3}\cdot \frac{sinx}{cos^2x}\\\\y'=\frac{1}{3}\cdot \frac{(sinx)'\cdot cos^2x-sinx\cdot (cos^2x)}{(cos^2x)^2}=\frac{1}{3}\cdot \frac{cosx\cdot cos^2x-sinx\cdot 2cosx\cdot (-sinx)}{cos^4x}=\\\\=\frac{1}{3}\cdot \frac{cosx\cdot (cos^2x+2sin^2x)}{cos^4x}=\frac{cos^2x+2sin^2x}{3\, cos^3x}=\frac{(cos^2x+sin^2x)+sin^2x}{3\, cos^3x}=\frac{1+sin^2x}{3\, cos^3x}$