If x² + xy – 3y = 3, then at the point (2, 1), dy/dx (A) 5
(B) 4
(C) 7/3 (D) 2

A

Step-by-step explanation:

We are given the equation:  

And we want to find dy/dx at the point (2, 1).

Find dy/dx. We can take the derivative of both sides with respect to x:

Implicitly differentiate:

Solve for dy/dx:

To find dy/dx at (2, 1), evaluate dy/dx for x = 2 and y = 1. Hence:

Hence, our answer is A.

We want to find the differential dy/dx for the given expression at the given point. We will see that the correct option is A.

We have:

x^2 + xy - 3y = 3

First, we need to isolate the variable y in one side of the equation, so we get:

xy - 3y = 3 - x^2

y*(x - 3) = 3 - x^2

y = (x - x^2)/(x - 3)

Now we can differentiate this, remember that if:

f(x) = g(x)*h(x)

then:

f'(x) = g(x)*h'(x) + g'(x)*h'(x)

Using that rule.

dy/dx = (1 - 2x)/(x - 3) - (x - x^2)/(x - 3)^2

Now we need to evaluate this in x = 2 (the x-value of the point) so we get:

(1 - 2*2)/(2 - 3) - (2 - 2^2)/(2 - 3)^2

= (-3)/(-1) - (-2)/(1) = 5

So the correct option is A.

If you want to learn more about differentiation, you can read:

link

step-by-step explanation:

the options are kind of confusing. i can tell you what i see going on here when i look at the graph.

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