Question

find the derivative of x^2/root x-4

Answer 1

\[\frac{ d }{ dx }(\frac{ x ^{2} }{ \sqrt{x -4)} })=?\]This is your question, correct?

Answer 2

yes

Answer 3

OK then first rewrite as\[y =\frac{ x ^{2} }{ (x -4)^{\frac{ 1 }{ 2 }} }\]and use the quotient rule, or rewrite as\[y =x ^{2}(x -4)^{-\frac{ 1 }{ 2 }}\]and use the product rule. Which rule is your preference?

Answer 4

i used the quotient rule and got (root x-4) (2x)-(x^2)-(1/2root x-4)/ (root x-4)^2. And now I don't know what to do from here... I don't know if i'm using the quotient right or not.

Answer 5

Which means so far you got\[\frac{ dy }{ dx }=\frac{ 2x \sqrt{x -4}+\frac{ x ^{2} }{ 2\sqrt{x -4} } }{ x -4 }\]Understand?

Answer 6

yeah

Answer 7

wait isn't it suppose to be a minus in the middle of the numerator instead of the add? Why are you adding?

Answer 8

negative times a negative, or a negative divided by a negative equals positive. Right?

Answer 9

whoops, made a mistake my previous answer is suppose to be (root x-4) (2x)-(x^2)(1/2root x-4)/(root x-4)^2. There is technically no negatives.

Answer 10

only the minus sign due to the quotient rule.

Answer 11

Oh yes you're right actually, it is a minus sign.

Answer 12

\[\frac{ dy }{ dx }=\frac{ 2x \sqrt{x -4}-\frac{ x ^{2} }{ 2\sqrt{x -4} } }{ x -4 }\]

Answer 13

OK now you need to simplify this. Do you know how?

Answer 14

no...that's where i'm having trouble at.

Answer 15

multiply top and bottom by \(2\sqrt{x-4}\) and it will simplify like mad

Answer 16

As satellite said, multiply both the numerator and the denominator by\[2\sqrt{x -4}\]

Answer 17

is it 4(x-4)-x^2/x(x-4)^3/2?

Answer 18

No, it's\[\frac{ dy }{ dx }=\frac{ 4x(x -4)-x ^{2} }{ 2\sqrt{(x -4)^{3}} }\]

Answer 19

The exponent to the root in the denominator is a 3. The equation feature makes it difficult to distinguish between exponents 2 and 3. Alright?

Answer 20

okay, now what?

Answer 21

Simplify the numerator. Apply the distributive property and collect like terms.

Answer 22

\[\frac{ dy }{ dx }\frac{ 4x ^{2}-16x -8x ^{2} }{ 2\sqrt{(x -4)^{3}} }\]

Answer 23

Now please tell me that you at least know how to collect like terms in the numerator.

Answer 24

yes I do. Thank you so so much for your help!

Answer 25

There should be an equal sign there. I must have inadvertently missed it.

Answer 26

Welcome!