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Solution assignment 24 Chain rule

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Assignment 24

Differentiate:

y = e^{\sqrt[3]{{4x + 1}}}

Solution

Differentiating this function requires a double chain rule, as we will see (the 'quote' means: the derivative of):

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

=\displaystyle\frac{{4e^{\sqrt[3]{{4x + 1}}} }}{{3\sqrt[3]{{(4x + 1)^2 }}}}

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