How do you differentiate sin^3 x?

lotejadaialy

lotejadaialy

Answered question

2023-03-25

How to differentiate sin 3 x ?

Answer & Explanation

kokheleka36tx

kokheleka36tx

Beginner2023-03-26Added 7 answers

step 1
In order to differentiate sin 3 ( x ) , we need to use a chain rule, which tells us that
d d x [ f ( g ( x ) ) ] = f ( g ( x ) ) g ( x )
Letting y = sin 3 ( x ) , thus
d y d x = 3 sin 2 ( x ) cos x
step 2
In this problem, we've also performed the power rule, namely by subtracting 1 from the power of 3 on the sin x term, which is why we end up with a sin 2 ( x ) .
Therefore, d y d x = 3 sin 2 ( x ) cos x

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