Differentiating wrt time

Questions
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1

i have to differentiate a*cos(alpha) wrt time. alpha is a function of time whereas a is not. If i use Dt function in-built in Mathemtica, it will automatically give assume a to be also a function of time. How to get around this problem?

2

I usually find it easiest to put the dependency on t into the object or not as in

In[1]:= a Cos[alpha[t]]
        
Out[1]= a Cos[alpha[t]]
        
In[2]:= D[%, t]
        
Out[2]= -(a Sin[alpha[t]] alpha'[t])

But you can also just define the derivative of a to be zero with respect to t before you do anything.

3

That helps a lot. Thanks.