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AP Calculus Tutorial! | Implicit Differentiation + 4 Examples
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In this video I introduce implicit differentiation and work out some good examples.
The idea behind implicit differentiation is that we no longer have an equation that looks like "y = some function of x" (y is explicitly in terms of x). Instead, we have x terms and y terms mixed up on both sides of the = sign.
So what we can do is differentiate both sides with respect to x, but when we differentiate a "y" term, we have to use the chain rule and multiply that y term by the derivative of y with respect to x, which is dy/dx. We then use algebra to solve for dy/dx, and that is the derivative of an equation that is implicitly in terms of x.
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The idea behind implicit differentiation is that we no longer have an equation that looks like "y = some function of x" (y is explicitly in terms of x). Instead, we have x terms and y terms mixed up on both sides of the = sign.
So what we can do is differentiate both sides with respect to x, but when we differentiate a "y" term, we have to use the chain rule and multiply that y term by the derivative of y with respect to x, which is dy/dx. We then use algebra to solve for dy/dx, and that is the derivative of an equation that is implicitly in terms of x.
FOLLOW ME ON SOCIAL MEDIA!!
IG @allmond_withthesauce
Twitter @Allmond_wtSauce
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