Den deriverte til en konstant funksjon

$$ $ \begin{array}{rcl}{f}^{\text{'}}\left(x\right)& =& \underset{∆x\to 0}{\lim }\frac{f\left(x+∆x\right)-f\left(x\right)}{∆x}\end{array}$$$

$$ \begin{array}{rcl}f\left(x\right)& = & \mathrm{\pi }\\ & & \\ {\mathrm{f}}^{\text{'}}\left(x\right)& =& \underset{∆x\to 0}{\lim }\frac{\mathrm{f}\left(x+∆x\right)-\mathrm{f}\left(x\right)}{∆x}\\ & & \\ {\mathrm{f}}^{\text{'}}\left(x\right)& =& \underset{∆x\to 0}{\lim }\frac{\mathrm{\pi }-\mathrm{\pi }}{∆x}=0\end{array}$$

a) $$ \begin{array}{rcl}f\left(x\right) & =& 5\\ f^{\text{'}}\left(x\right) & =& 0\end{array}$$

b) $$ \begin{array}{rcl}y & =& e\\ y^{\text{'}} & =& 0\end{array}$$

c) $$ \begin{array}{rcl}g\left(x\right) & =& \mathrm{\pi }+5\\ g^{\text{'}}\left(x\right) & =& 0\end{array}$$

d) $$ \begin{array}{rcl} h\left(x\right) & =& 5{\mathrm{\pi }}^3\\ h^{\text{'}}\left(x\right) & =& 0\end{array}$$

e) $$ \begin{array}{rcl}i\left(x\right) & =& 2b\\ i^{\text{'}}\left(x\right) & =& 0\end{array}$$

f) $$ \begin{array}{rcl}j\left(x\right) & =& x+d\\ j^{\text{'}}\left(x\right) & =& 1\end{array}$$

g) $$ \begin{array}{rcl}k\left(x\right) & =& 3y+8\\ k^{\text{'}}\left(x\right) & =& 0\end{array}$$

Vi tegner $$ f\left(x\right)$$ med digital graftegner:

Åpne bilde i et nytt vindu

CC BY-SA

Bilde: Viveca Thindberg

Stigningstallet til $$ f\left(x\right)$$ er lik 0. Det kan man finne med digital graftegner, se bildet over der $$ a = 0$$. Når stigningstallet er 0, har grafen ingen positiv eller negativ stigning. Den er 0 for hele $$ f\left(x\right).$$