Answer:
6x·sin(x²)²·cos(x²)
Explanation:
You want the derivative of sin(x²)³.
Power rule
The power rule can be used.
(u^n)' = n·u^(n-1)·u'
Sine
The derivative of the sine function is ...
sin(v)' = cos(v)·v'
Expression
Here, we have u=sin(x²), and we want (u³)' with u' = cos(x²)·2x
(u³)' = 3u²·u'
(sin(x²)³)' = 3·sin(x²)²·cos(x²)·2x
The derivative is ...
6x·sin(x²)²·cos(x²)
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