Question

Assume ( x ) and ( y ) are functions of ( t ). Evaluate dy/d t for the following.

y³=2 x³+11 ; dx/dt=3, x=2, y=3 . What is dy/dt ? (Round to two decimal places as needed.)

Answer 1

To find dy/dt, differentiate the given equation y³=2x³+11 with respect to t using the chain rule. Substitute the given values of x=2, y=3, and dx/dt=3 into the equation to find dy/dt=2.67.

Step-by-step explanation:

To find dy/dt, we first need to differentiate the given equation y³=2x³+11 with respect to t using the chain rule.

Starting with y³=2x³+11, we take the derivative of both sides:

3y²(dy/dt) = 6x²(dx/dt)

Substituting the given values of x=2, y=3, and dx/dt=3 into the equation, we get:

3(3²)(dy/dt) = 6(2²)(3)

Simplifying further, we have:

27(dy/dt) = 72

Dividing both sides by 27, we find that:

dy/dt = 72/27 = 2.67