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Find the implicit derivative $\frac{d}{dx}\left(x\sqrt{1+y}+\sqrt{y\left(1+2x\right)}=2x\right)$

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 Solution

 Videos

Implicit differentiation | Advanced derivatives | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=mSVrqKZDRF4

Calculus - Take the log of both sides to find the derivative, y = (x(x^2 + 1)^2)/(sqrt(2x^2 - 1))

https://www.youtube.com/watch?v=7aF6Ck6ZRxw

Calculus - Find the derivative of natural logarithm using product property, d(ln(2x))/dx

https://www.youtube.com/watch?v=urYZhqwUTI0

Algebra 2 - Finding the vertex of a quadratic function y = 2x^2 + 2x + 1

https://www.youtube.com/watch?v=V2udel2WylU

Worked example: Evaluating derivative with implicit differentiation | AP Calculus AB | Khan Academy

https://www.youtube.com/watch?v=KyYC8XzKsHU

Algebra 2 - How to find the real zero of a cubic function, y = -1(x - 3)^3 + 1

https://www.youtube.com/watch?v=4dSA02Fzric

Main Topic: Definition of Derivative

Resolution of derivatives using the definition of the derivative, which is the limit of difference quotients of real numbers.

Find the implicit derivative $\frac{d}{dx}\left(x\sqrt{1+y}+\sqrt{y\left(1+2x\right)}=2x\right)$

Related Videos

 Solution

 Videos

Implicit differentiation | Advanced derivatives | AP Calculus AB | Khan Academy

Calculus - Take the log of both sides to find the derivative, y = (x(x^2 + 1)^2)/(sqrt(2x^2 - 1))

Calculus - Find the derivative of natural logarithm using product property, d(ln(2x))/dx

Algebra 2 - Finding the vertex of a quadratic function y = 2x^2 + 2x + 1

Worked example: Evaluating derivative with implicit differentiation | AP Calculus AB | Khan Academy

Algebra 2 - How to find the real zero of a cubic function, y = -1(x - 3)^3 + 1

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Main Topic: Definition of Derivative

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