Question

find dy/dx if x√x + y√y = a√a​

Answer 1

Answer:

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Step-by-step explanation:

dydx=−(yx)13

Explanation:

We will differentiate implicitly. This means, that whenever we differentiate a variable that's not x, the chain rule will kick in. Take a look at a couple examples before starting here:

   ddxx3=3x2 but  ddxy3=3y2dydx

   ddxx=1 but  ddxy=dydx

   ddxxy2=(ddxx)y2+x(ddxy2)=y2+x(2y)dydx

So, for the given example, we see that we will use the power rule on the left-hand side. On the right, don't be misled by the two-thirds power: a23 is still a constant.

   ddx(x23+y23)=ddxa23

Power rule:

   23x−13+23y−13dydx=0

Multiply both sides by 32:

   x−13+y−13dydx=0

   1x13+1y13dydx=0

Solving for dydx:

   1y13dydx=−1x13

   dydx=−y13x13=−(yx)13=−3√yx

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