Help with working out the gradient.

Phoenix08

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I do not know what to do for these last two questions. I’m not in the best state of mind to do mathematics, but this is due in by midnight. Even if I do not work it out in time, I’d like to know how to do it for next time.
 

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I do not know what to do
Hi Phoenix. The first derivative is a function that outputs its source function's gradients. Determine the first derivative of each function given. For part (b), evaluate the derivative when x=4. In part (c), evaluate the derivative when x=-3.

Your image cuts off the instruction given for part (b). Please provide the missing information. I'm not familiar with the definition of "top heavy", but it may imply that you're supposed to use an approximating method. Can you also explain how your class taught you to find derivatives? If you need more help, please share your efforts so far, so that we can see what you're doing. Cheers!

:)
  \;
 
Hi Phoenix. The first derivative is a function that outputs its source function's gradients. Determine the first derivative of each function given. For part (b), evaluate the derivative when x=4. In part (c), evaluate the derivative when x=-3.

Your image cuts off the instruction given for part (b). Please provide the missing information. I'm not familiar with the definition of "top heavy", but it may imply that you're supposed to use an approximating method. Can you also explain how your class taught you to find derivatives? If you need more help, please share your efforts so far, so that we can see what you're doing. Cheers!

:)
  \;
Give your answer as a too heavy fraction in the form value/value.
 
Hi Phoenix. The first derivative is a function that outputs its source function's gradients. Determine the first derivative of each function given. For part (b), evaluate the derivative when x=4. In part (c), evaluate the derivative when x=-3.

Your image cuts off the instruction given for part (b). Please provide the missing information. I'm not familiar with the definition of "top heavy", but it may imply that you're supposed to use an approximating method. Can you also explain how your class taught you to find derivatives? If you need more help, please share your efforts so far, so that we can see what you're doing. Cheers!

:)
  \;
It means that the number at the top is larger than the number at the bottom.
 
I do not know what to do for these last two questions. I’m not in the best state of mind to do mathematics, but this is due in by midnight. Even if I do not work it out in time, I’d like to know how to do it for next time.
A "top-heavy fraction" is also called an improper fraction; all they mean there is not to write the answer as a mixed number or a decimal, but to leave it in fraction form.

The important thing is that you need to differentiate, and you haven't said what part of that you find difficult. Both can be done using the quotient rule, so I suspect that is what you are learning; the first can be done more easily by carrying out the division (dividing each term of the numerator by x) and then differentiating term by term. You could do the same with the second, with a little more work, since you have to expand the numerator.

Please show us what you have tried and where you got stuck.
 
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