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Solution assignment 30 Chain rule

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Assignment 30

Differentiate:

y=\sin[(4x+5)^{0.6}]

Solution

We need to use the informal chain rule twice (the 'quote' means: the derivative of):

y'=\cos [(4x + 5)^{0.6} ]\cdot[(4x + 5)^{0.6} ]'=

=\cos [(4x + 5)^{0.6} ]\cdot(0.6).(4x + 5)^{ - 0.4} \cdot(4x + 5)'=

=\displaystyle\frac{{2.4\cos [(4x + 5)^{0.6} ]}}{{(4x + 5)^{0.4} }}

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