Question

Assume x and y are functions of t. Evaluate dy/dt. xy+x=12; dx/dt = -3, x=2, y=5

Answer 1

So if you take the derivative of this function, you get (dx/dt)(y) + (dy/dt)(x) + (dx/dt) = 0. Plug in dx/dt, x, and y into the function. (-3)(5) + (2)(dy/dt) + (-3) = 0. Isolate dy/dt. 2dy/dt = 18, so dy/dt = 9.

Answer 2

Differentiate the function xy + x = 12 with respect to t. Then the value of dy/dt will be 9.

What is differentiation?

The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.

The function is given below.

xy + x = 12

dx/dt = -3, x = 2, y = 5

Then the value of dy/dt will be

Differentiate the function with respect to t. Then we have

$\rm x\dfrac{dy}{dt} + y\dfrac{dx}{dt} + \dfrac{dx}{dt} = 0$

Then put the value, then we have

2 (dy/dt) + 5 (-3) + (-3) = 0

        2 (dy/dt) - 15 – 3 = 0

                        (dy/dt) = 18 / 2

                        (dy/dt) = 9

More about the differentiation link is given below.

https://brainly.com/question/24062595

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