Question

differetiate sin2x^2​

Answer 1

Answer:

2sin4x

Explanation:

differentiate using the chain rule

∣∣ ∣ ∣∣¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯aaddx(f(g(x)))=f'(g(x))g'(x)aa∣∣∣−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−........(A)

here f(g(x))=sin2(2x)=(sin2x)2

⇒f'(g(x))=2sin2x

Note, 2 applications of chain rule required for g'(x)

g(x)=sin2x⇒g'(x)=cos2x.ddx(2x)=2cos2x
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Substitute these values into (A)

2sin2x.2cos2x=4sin2xcos2x

Reminder∣∣ ∣∣¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯aasin4x=2sin2xcos2xaa∣∣−−−−−−−−−−−−−−−−−−−−−−−−

⇒ddx(sin2(2x))=4sin2xcos2x=2sin4x

Answer 2

Answer:

Step-by-step explanation:

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