[4/4 Points] DETAILS PREVIOUS ANSWERS PREVIOUS ANSWERS LARCALC11 2.6.005. MY NOTES PRACTICE ANOTHER Assume that x and y are both differentiable functions of t and find the required values of dy//dt and dx//dt. xy=6 (a) Find dy//dt, given x=6 and dx//dt=13.

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[4/4 Points] DETAILS PREVIOUS ANSWERS PREVIOUS ANSWERS LARCALC11 2.6.005.  MY NOTES PRACTICE ANOTHER Assume that  x and  y are both differentiable functions of  t and find the required values of  dy//dt and  dx//dt.  xy=6 (a) Find  dy//dt, given  x=6 and  dx//dt=13.

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Differentiate equation with respect to t: Differentiate both sides of the equation xy=6 with respect to t. Using the product rule for differentiation, we get d(xy)/dt = d(6)/dt. This simplifies to x(dy/dt) + y(dx/dt) = 0, since the derivative of a constant is 0.Substitute given values: Substitute the given values into the differentiated equation. We know that x=6 and dx/dt=13. So we substitute these values into the equation from Step 1 to get: 6(dy/dt) + y(13) = 0.Solve for dy/dt: Solve for dy/dt. We need to express y in terms of x using the original equation xy=6. Since x=6, we have 6y=6, which means y=1. Now we substitute y=1 into the equation from Step 2 to get: 6(dy/dt) + 1(13) = 0.Isolate dy/dt: Isolate dy/dt. To isolate dy/dt, we subtract 13 from both sides of the equation: 6(dy/dt) = -13. Now, divide both sides by 6 to solve for dy/dt: dy/dt = -13/6.

Assume that $x$ and $y$ are both differentiable functions of $t$ and find the required values of $\frac{dy}{dt}$ and $\frac{dx}{dt}$ . $xy=6$ $\newline$ (a) Find $\frac{dy}{dt}$ , given $x=6$ and $\frac{dx}{dt}=13$ .

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Assume thatxxx and yyy are both differentiable functions of ttt and find the required values of dydt\frac{dy}{dt}dtdy​ and dxdt\frac{dx}{dt}dtdx​.xy=6xy=6xy=6\newline(a) Find dydt\frac{dy}{dt}dtdy​, given x=6x=6x=6 anddxdt=13\frac{dx}{dt}=13dtdx​=13.

Assume that $x$ and $y$ are both differentiable functions of $t$ and find the required values of $\frac{dy}{dt}$ and $\frac{dx}{dt}$ . $xy=6$ $\newline$ (a) Find $\frac{dy}{dt}$ , given $x=6$ and $\frac{dx}{dt}=13$ .