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And so this whole expression over here, so I can write the second derivative of y with respect to x is going to be equal to, well we know that that's going to be equal to 1/4. 1/4 times three times one squared, which is just three

And now I can divide both sides by two y, and I am going to get that the derivative of y with respect to x is equal to x, x over y. Now, the next step is let's take the derivative of both sides of this with respect to x, and then we can hopefully find our second derivative of y with respect to x. And to help us there, actually let me rewrite this.

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Example: Using Implicit Differentiation and the Product Rule Assuming that y y is defined implicitly by the equation x3siny+y =4x+3 x 3 sin y + y = 4 x + 3, find dy dx d y d x. Show

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