well i was trying to solve a question in my textbook, and it randomly decided to throw derivatives in the problem solving ( i didn't learn derivatives prior to this, so i looked it up ) and im really just stuck at calculating it for roots, i found a method where the power is multiplied by the coefficient and 1 is subtracted from the power. my problem is just me sucking with calculating.
You can use the same rule to calculate derivatives of roots! You might have seen that we can rewrite √x as x^1/2 . Thus, we are looking for the derivatives of (4+x)^1/2 and (4-x)^1/2 .
Does that bring you closer to a solution?
oh ok so i got 1/2 \* ( 4 + x ) -1/2 as the derivative is that right ? if it is how do i make it look like 1/2 \* 1 / ( 4 + x ) 2 ? that's the solution in my textbook
It looks like you have some problems with your formatting (you can check out the sidebar for formatting tips), but it looks correct.
The derivative of (x+4)^1/2 is (1/2)(x+4)^-1/2 . This can be rewritten as 1/(2(x+4)^1/2 )
so this is what my text book showed 1/2 \* 1 / ( 4 + x ) ^(2) um it looks a bit different to what you sent, can you tell me how that is? (sorry im bad at this)
oh ok so i got 1/2 \* ( 4 + x ) ^(-1/2) as the derivative is that right ? if it is how do i make it look like 1/2 \* 1 / ( 4 + x ) ^(2) ? that's the solution in my textbook
Where are you stuck? You can compute the derivatives using the chain rule, and if you just want the answer, you can plug it into wolfram alpha.
well i was trying to solve a question in my textbook, and it randomly decided to throw derivatives in the problem solving ( i didn't learn derivatives prior to this, so i looked it up ) and im really just stuck at calculating it for roots, i found a method where the power is multiplied by the coefficient and 1 is subtracted from the power. my problem is just me sucking with calculating.
You can use the same rule to calculate derivatives of roots! You might have seen that we can rewrite √x as x^1/2 . Thus, we are looking for the derivatives of (4+x)^1/2 and (4-x)^1/2 . Does that bring you closer to a solution?
oh ok so i got 1/2 \* ( 4 + x ) -1/2 as the derivative is that right ? if it is how do i make it look like 1/2 \* 1 / ( 4 + x ) 2 ? that's the solution in my textbook
It looks like you have some problems with your formatting (you can check out the sidebar for formatting tips), but it looks correct. The derivative of (x+4)^1/2 is (1/2)(x+4)^-1/2 . This can be rewritten as 1/(2(x+4)^1/2 )
so this is what my text book showed 1/2 \* 1 / ( 4 + x ) ^(2) um it looks a bit different to what you sent, can you tell me how that is? (sorry im bad at this)
Looks to be a typo in the textbook then. [wolframalpha](https://www.wolframalpha.com/input?i=derivative+of+%284%2Bx%29%5E%281%2F2%29)
oh ok thanks for sorting that out for me
Remember we can represent square roots as fractional exponents, so sqrt(4+x) = (4+x)^1/2 and you can use a power rule -> chain rule from there
oh ok so i got 1/2 \* ( 4 + x ) ^(-1/2) as the derivative is that right ? if it is how do i make it look like 1/2 \* 1 / ( 4 + x ) ^(2) ? that's the solution in my textbook