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How to differentiate sin³x² ?

1 Answer

6 votes

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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User Adi Barda
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