# Differentialregnings regler

Differential regne regler

 $$f(x)$$ $$f^{,}(x)$$ $$f(x)=k$$ $$f^{,}(x) = 0$$ $$f(x)=a \cdot x$$ $$f^{,}(x) = a$$ $$f(x)={x^n}$$ $$f^{,}(x)=n \cdot {x^{n-1}}$$ $$f(x)={a^x}$$  $$a >0,a \neq 1$$ $$f^{,}(x)=ln \cdot a \cdot {a^x}$$ $$f(x)=cos(x)$$ $$f^{,}(x)=-sin(x)$$ $$f(x)=sin(x)$$ $$f^{,}(x)=cos(x)$$ $$f(x)=tan(x)$$ $$f^{,}(x)=1+{\left(tan(x)\right)^2}={\left(cos(x)\right)^{-2}}$$ $$f(x)=ln(x)$$ $$f^{,}(x) = {x^{-1}}$$ $$f(x)=log(x)$$ $$f^{,}(x) = \left( x \cdot ln10\right)^{-1}$$ $$f(x)=log_{\it a}(x)$$ (hvor a er logaritmens grundtal) $$f^{,}(x) = \left( x \cdot ln(a)\right)^{-1}$$ $$f(x)={e^x}$$ $$f^{,}(x) = {e^x}$$

Se også
Differential-ligninger
Integral-regneregler