<s>[INST] Derivative of $10^x\cdot\log_{10}(x)$ 
Derive  $10^x\cdot\log_{10}(x)$ 

$$10^x\cdot \ln(10)\cdot \log_{10}(x)+\frac{1}{x\cdot \ln(10)}\cdot 10^x$$
But WolframAlpha gives another solution. Where am I wrong?
 [/INST] Using 
$$\log_{10}(x) = \frac{\ln(x)}{\ln(10)}$$
then 
\begin{align}
D \left[ 10^{x} \, \log_{10}(x) \right] &= D \left[ e^{x \, \ln(10)} \, \frac{\ln(x)}{\ln(10)} \right] \\
&= \frac{1}{\ln(10)} \, \left[ \frac{10^{x}}{x} + \ln(10) \, 10^{x} \, \ln(x) \right] \\
&= 10^{x} \, \left[ \frac{1}{ x \, \ln(10)} + \ln(10) \, \log_{10}(x) \right]
\end{align}
</s>