Question

Derivar

f(x) = sen(x-1/x^2+1)

Answer 1

$<var> \\f(x)=\sin\frac{x-1}{x^2+1}\\ f'(x)=\cos\frac{x-1}{x^2+1}\cdot\frac{x^2+1-(x-1)\cdot2x}{(x^2+1)^2}\\ f'(x)=\frac{x^2+1-2x^2+2x}{(x^2+1)^2}\cos\frac{x-1}{x^2+1}\\ f'(x)=\frac{-x^2+2x+1}{(x^2+1)^2}\cos\frac{x-1}{x^2+1}\\ f'(x)=-\frac{x^2-2x-1}{(x^2+1)^2}\cos\frac{x-1}{x^2+1}\\ </var>$