Suppose f(x) is differentiable function and if f(x)y + f(y)x = 10, find f'(x).
Question:
Suppose f(x) is differentiable function and if f(x)y + f(y)x = 10, find f'(x).
Implicit Differentiation:
Here we will need to take a derivative to find {eq}f'(x). {/eq} However, {eq}f(x) {/eq} is not explicitly isolated, so we must differentiate implicitly. To do this we take the derivative as we know how, but then multiply by {eq}\dfrac{dy}{dx} {/eq} every time we differentiate a term with {eq}y. {/eq}
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Implicit Differentiation Technique, Formula & Examples
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Chapter 6 / Lesson 5
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Explicit differentiation is used when 'y' is isolated, whereas implicit differentiation can be used similar to the chain rule when 'y' is not isolated. Learn more about implicit differentiation through examples of formulas and graphs.
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