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Find {eq}y'' {/eq} for {eq}x^2 + 6 x y - 2 y^2 = 3 {/eq}.

Question:

Find {eq}y'' {/eq} for {eq}x^2 + 6 x y - 2 y^2 = 3 {/eq}.

Implicit Differentiation:

Implicit differentiation is a special type of differentiation method. It is same as chain rule. It is special case of differentiation. If a function is in the form {eq}F(g(x)) {/eq}, then its derivative will be derivative of outer function {eq}F {/eq} multiplied by the derivative of inner function {eq}g(x) {/eq} i.e. final derivative will be {eq}F'(g(x))\times g'(x) {/eq}

Answer and Explanation: 1

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{eq}\displaystyle x^2+6xy-2y^2=3 {/eq}

Differentiating we get:

{eq}\displaystyle 2x+6y+6x\frac{dy}{dx}-4y\frac{dy}{dx}=0 {/eq}

{eq}\displaystyl...

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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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