Differentiating y with respect to x when the given function has no x

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Mackattack

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I typed it in Symbolab and got zero. Will zero always be the answer when the variable mentioned in the function doesn't respect x? Can the answer not be expressed in terms of t or just changed to x?

I'm asking 'cause my worksheet is filled with functions not containing x (all problems in my worksheet are asking for the derivative of the function with respect to x). In previous lectures given to me by my teacher, the variable was always x. It's only in this worksheet where he changed the variables.
 
Unless t is a function of x, you treat t like a constant. So if you y=tx, then dy/dx = t. Now if t is a function of x, then you use the chain rule. For example, if t=2x+4, y = t^2, the dy/dx = 8x+16
 
Mackattack said:
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I typed it in Symbolab and got zero. Will zero always be the answer when the variable mentioned in the function doesn't respect x? Can the answer not be expressed in terms of t or just changed to x?

I'm asking 'cause my worksheet is filled with functions not containing x (all problems in my worksheet are asking for the derivative of the function with respect to x). In previous lectures given to me by my teacher, the variable was always x. It's only in this worksheet where he changed the variables.
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It seems that you are giving us a snippet of the worksheet! It may be that 'x' is a function of 't' too.

Can you post an image of the ENTIRE worksheet?
 
I suspect that the problems that have t in them should be asking to find the derivative with respect to t and not x. It is just a (bad) typo.
 
Since it does say what it says you should put down 0 for #1, 2, 3, 5, 6

However for practice you should find the derivative.
 
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Jomo said:
I suspect that the problems that have t in them should be asking to find the derivative with respect to t and not x. It is just a (bad) typo.
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Really bad typo indeed, but the last time I argued with my teacher that he made a typo, he told me that he intended that and was testing us. He gave deductions to all who automatically corrected his typo. Enough about that story. Thank you for your reply.
 
Mackattack said:
Really bad typo indeed, but the last time I argued with my teacher that he made a typo, he told me that he intended that and was testing us. He gave deductions to all who automatically corrected his typo. Enough about that story. Thank you for your reply.
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No, no, no! I would never correct a teachers typo. Personally I think it is rude to rewrite a teacher's question. As I said, you should put 0 for all those problems and for practice take the derivative wrt t.
 
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Mackattack said:
Really bad typo indeed, but the last time I argued with my teacher that he made a typo, he told me that he intended that and was testing us. He gave deductions to all who automatically corrected his typo. Enough about that story. Thank you for your reply.
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What I always recommend is to give the answer to the problem as stated, with an explanation (e.g. "taking t as a constant"), and then also say, "If the problem had been to find dy/dt, then ... ". Never solve a problem different from what is written without at least stating that you are changing it. If you do all this, you should get extra credit rather than a deduction.

(Of course, this is appropriate mostly in a case like this, where the answer to the stated problem is trivial, and there is enough time to solve the alternative problems. If fewer than half of the problems had this issue, I would be more likely to assume that it is intentional, and just give the 0's, with explanation, and not bother with the alternative.)
 
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