regole di derivazione

• $\frac{d}{dx}\left(f(x)\pm g(x)\right)=f^{\prime }(x)\pm g^{\prime }(x)$.
• $\frac{d}{dx}\left(f(x)\cdot g(x)\right)=f^{\prime }(x)\cdot g(x)+f(x)\cdot g^{\prime }(x)$.
• $\frac{d}{dx}\left(\frac{f(x)}{g(x)}\right)=\frac{f^{\prime }(x)\cdot g(x)-f(x)\cdot g^{\prime }(x)}{(g(x){)}^2}$.
• $\frac{d}{dx}\left(f(g(x))\right)=f^{\prime }(g(x))\cdot g^{\prime }(x)$.
• $\frac{d}{dx}\left(f(x{)}^{g(x)}\right)=f(x{)}^{g(x)}\cdot \left(g^{\prime }(x)\ln (f(x))+\frac{g(x)\cdot f^{\prime }(x)}{f(x)}\right)$