At this point we provide a list of derivative formulas that may be obtained by applying the chain rule in conjunction with the formulas for derivatives of trigonometric functions. Their derivations are similar to those used in
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Using the chain rule with trigonometric functions
For all values of
for which the derivative is defined,
Combining the chain rule with the product rule
Find the derivative of
First apply the product rule, then apply the chain rule to each term of the product.
We can now combine the chain rule with other rules for differentiating functions, but when we are differentiating the composition of three or more functions, we need to apply the chain rule more than once. If we look at this situation in general terms, we can generate a formula, but we do not need to remember it, as we can simply apply the chain rule multiple times.
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