Find dy/dx by differentiating implicity.
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Find dy/dx by differentiating implicitly. When applicable, express the result in terms of x and y.
4(x^2 +2)^3 +(y^2+2)^2 = 19
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The expert determines dy/dx by differentiating implicitly.
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4(x^2 +2)^3 +(y^2+2)^2 = 19
To differentiate implicitly we differentiate even without knowing y as a function of x (i.e. y(x)).
We will differentiate with respect to x:
d/dx(4(x^2 +2)^3 +(y^2+2)^2 = 19)
Differentiation is linear so we can "distribute" or do each derivative separately:
d/dx(4(x^2 +2)^3) +d/dx((y^2+2)^2) = d/dx(19)
Let's take a look at the first derivative:
d/dx(4(x^2 +2)^3)
Recall the chain rule:
df/dx = df/du*du/dx
We can make another variable y and use this to use chain rule. We can also use other wording of the chain rule "the derivative of the outside times ...
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