Derivatives with Logarithms
d/dx ln x
1/x
d/dx e^x
e^x
\int \ 1/x dx
ln|x|+C
\int \ e^x dx
e^x +C
\int \ \cosx \ dx
\sin x \ +C
d/dx \cosx
-\sin x
d/dx ln(3x^2)
\frac{1}{3x^2} \cdot 6x
d/dx e^{x^2}
2xe^{x^2}
\int \ 6/{x+2} \ dx
6ln|x+2|+C
\int \ 3xe^{x^2} \ \dx
3/2 e^{x^2} +C
\int \ tanu \ du
-ln|cosu| +C
d/dx cotx
-csc^2x
d/dx ln|tanx|
1/tanx \cdot sec^2x
d/dx e^{lnx}
1
\int \ e^x/{1+e^x} \ dx
ln(1+e^x)+C
\int \ 2e^{2x+11} \ \dx
e^{2x-11} +C
\int \ secu \ du
ln|secu+tanu|+C
d/dx cscx
-cscxcotx