# Derivative an exponential function with base 10 in Wolfram|Alpha

Posted 4 months ago
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 I've long struggled with Wolfram|Alpha's interpreter, but today it's annoyed me particularly much, so I want to know how to trick it into giving me what I want. At the moment, I'm trying to differentiate a function. One step in doing this is finding $\frac{\partial}{\partial x} 10^{0.4x}$, which if I try in Wolfram|Alpha gives: $$\frac{\partial}{\partial x} 10^{0.4x} = 0.921034e^{0.921034x}\tag{1}$$ which is less than helpful, because I want it with base-10. A much more useful output would be: $$\frac{\partial}{\partial x} 10^{0.4x} = \ln{(10^{0.4})}10^{0.4x}\tag{2}$$ No matter what I try, though, I can't get it to output anything like Equation 2. Trying "d/dx 10^(0.4*x) without E" just ignores the last part, and trying "derivative of 10^(0.4*x) as a power of 10" adds a as a second variable! It's very frustrating that Wolfram|Alpha seems to ignore my (I think rather simple) instructions, which as I said is a long-standing issue I've had. What sort of commands do I need to input to trick Wolfram|Alpha into doing what I want it to?
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Posted 1 month ago
 I'm continuing to have trouble similar to what I described above. Now, however, I'm trying to integrate the expression: $\frac{\sum_{n=0}^N{\sin(nx)}}{\sum_{n=0}^N{(a_n + \cos(nx) + \sin(nx))}}\tag{1}$My input into Wolfram Alpha is: sum(sin(n*x)) from n = 0 to 1 / (sum(a_n + cos(n*x) + sin(n*x))) from n = 0 to 1. This gives exactly Equation 1 with N = 1, as expected, and changing N changes the sum.However, I can't get it to actually integrate this expression. Adding the word integrate in front somehow causes it to interpret the whole thing as (sin(n*x))! Adding the word antiderivative to the end instead causes it to try to integrate the denominator alone (and causes computation time to be exceeded, but that's a separate issue). Finally, putting the original expression in parentheses and adding the word integral to the end causes it to interpret the input as... sin.I really don't understand what I'm doing wrong. Please help.
 By manipulating the parens I think I got it to integrate for you Integrate (sum sin(n*x) from n = 0 to 1)/(sum a_n + cos(n*x) + sin(n*x) from n = 0 to 1) or even Integrate (sum sin n*x,n,0,1)/(sum a_n + cos n*x + sin n*x,n,0,1) WolframAlphaLink