f) Solve : \( \left(1+y^{2}\right) d x+x d y=\tan ^{-1} y d y \)

D': dyferent \( f(x)=\frac{3 x^{2}+2 x}{4 x^{2}+2 x} \)

1. Obtenga la derivada de cada función, usando la fórmula: \( \begin{aligned} f(x)=x^{2}\end{aligned} \) \( \begin{aligned}\text { [Res. }] f(x) & =\lim _{x \rightarrow-5} \frac{(x+h)^{2}-x^{2}}{h} \\ & =\lim _{x \rightarrow 0} \frac{2 x h+h^{2}}{h} \\ & =\lim _{x \rightarrow 0}(2 x+h) \\ & =2 x\end{aligned} \) (1) \( f(x)=2 x^{2} \) \( f(x)-5 i m \)

(28) \( \int \sin ^{5} x \sec x d x \)

\( \lim _ { x \rightarrow 0 } 2 x \cdot \ln ( x ) - 2 x \)

what is the rule of below inverse function? \[ f^{\prime}(x)=\frac{x}{\sqrt{x^{2}+1}} \]