Suppose
y = , where x and y are functions of t.
If dy/dt = 4, find dx/dt when x = 12.

The value of is 20

Explanation:

Given that the expression is

We need to determine the value of when

Value of :

Let us differentiate both sides of the equation with respect to t.

Thus, we have,

Applying the chain rule, we get,

Differentiating, we get,

Simplifying, we get,

Now, we shall determine the value of when

Substituting and , we have,

Simplifying the values, we get,

Thus, the value of is 20

20

Step-by-step explanation:

dy/dx = [½(2x + 1)^-½]×2

= 1/[(2x+1)^½]

At x = 12

1/(25^½) = 1/5

dy/dx = dy/dt × dt/dx

⅕ = 4 × dt/dx

dx/dt = 4 ÷ ⅕

= 4 × 5

= 20

explanation:

previous steps have made pa≅ pb ≅ st ≅ su. setting the compass width to ab allows you to make tu the same length. then δstu ≅ δpab by the sss congruence postulate, and ∠p ≅ ∠s by the reason cpctc.