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Solution assignment 28 Chain rule

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Assignment 28

Differentiate:

y=\displaystyle\frac{1}{\sqrt{5x+12}}

Solution

It is better to rewrite the function:

y=\displaystyle\frac{1}{(5x+12)^{\frac{1}{2}}}=(5x+12)^{-\frac{1}{2}}

Then we can apply the informal chain rule:

y'=-\displaystyle\frac{1}{2}(5x+12)^{-\frac{3}{2}}\cdot5=-\displaystyle\frac{5}{2(5x+12)\sqrt{5x+12}}

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