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Solution assignment 11 Chain rule

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Assignment 11

Differentiate:

y=\sqrt[4]{4x^2+6x+2}

Solution

First write this function as a power function:

y=(4x^2+6x+2)^{\frac{1}{4}}

and apply the informal chain rule (the 'quote' means: the derivative of):

y'=\displaystyle\frac{1}{4}(4x^2+6x+2)^{-\frac{3}{4}}\cdot(4x^2+6x+2)'=\displaystyle\frac{8x+6}{4\sqrt[4]{(4x^2+6x+2)^3}}

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