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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.

Posted 1 month ago

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

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