Chain Rule:
Derivative of sin( sin(4x) )
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Find the derivative of
What part of this do we work on first?
Since we work from the outside in, we differentiate the sine first.
Do we need to use the Chain Rule ?
Yes, since the argument of the sine function is more complex than just "x".
This problem may become clearer if we substitute a new variable
Equation 1
Rewrite the problem in terms of this variable.
Carry out the differentiation with respect to u.
Equation 2
Are we done?
No.
What must we do next?
We need to determine
.
Do that.
Using
, we get
Equation 3
We want a result in terms of x, our original variable. How can we get that?
We can substitute equations 1 and 3 into equation 2.
Do that.
We get
Be sure to distinguish this problem from
. Just to be sure, find this derivative.
Carefully note where this result is different.
The end. If you found this helpful and would recommend that I create more pages like this one, please let me know: Email to John Taylor