summen-und-faktor-regel

$$||"id":485664984278||f(x)=c{f}^{\prime }(x)=0f(x)=n^n{f}^{\prime }(x)=n\ast x^{n-1}f(x)=e^x{f}^{\prime }(x)=e^{x}f(x)=\ln x{f}^{\prime }(x)=\frac{1}{x}f(x)={\log }_{10}x{f}^{\prime }(x)=\frac{1}{x\ast \ln 10}f(x)=a^x{f}^{\prime }(x)=a^x\ast \ln a$$

faktorregel:

$(c\ast f{)}^{\prime }=c\ast f^{\prime }$

summenregel:

$(f\pm g{)}^{\prime }=f^{\prime }\pm g^{\prime }$

fakorregel bsp

die klammer dient, um zu zeigen, was noch nicht abgeleitet wurde

$$||"id":1244981010890||f_1(x)=3\ast x^2{f}_1^{\prime }(x)=(3\ast x^2{)}^{\prime }{f}_1(x)=3\ast (x^2{)}^{\prime }{f}_1^{\prime }(x)=3\ast 2x{f}_1^{\prime }(x)=6x$$

summenregel bsp

$$||"id":1080551024286||f_2(x)=e^x+d{f}_2^{\prime }(x)=(e^x+d{)}^{\prime }{f}_2^{\prime }(x)=(e^x{)}^{\prime }+(d{)}^{\prime }{f}_2^{\prime }(x)=e^x+0f_2^{\prime }(x)=e^x$$