Question

Question 12 I really need help cannot understand this question

Answer 1

First we can isolate y:

`\begin{gathered} x^2+xy=10 \\ xy=10-x^2 \\ y=(10)/(x)-x \\ y=10x^(-1)-x \end{gathered}`

To derive that, we can do it term by term, using the power rule:

`(d)/(dx)(x^n)=nx^(n-1)`

So:

`(dy)/(dx)=10(-1)x^(-1-1)-(1)x^(1-1)=-10x^(-2)-1^{}`

Now we substitute x = 2:

`(dy)/(dx)(x=2)=-10(2)^(-2)-1=-(10)/(4)-1=-(5)/(2)-(2)/(2)=-(7)/(2)`

So the answer is alternative A.