Question

differentiate f(x)=(1+sin^9(2x+3))^2​

Answer 1

Differentiate f(x) = (x3+1)2.

The only way we have of doing this so far is by first multiplying out the brackets and then differentiating. If we do this we get

f(x) = x6 + 2x3 +1 and therefore f´(x) = 6x5 +6x2.

This is no problem with a simple example such as the one above but what happens if we have for example f(x) = (x3+1)6 ?

In this case it takes far too much effort to multiply out the brackets before differentiating.

To differentiate composite functions like this we use what is called the Chain Rule. We'll do example 1 again to see how it works.

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