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jok3333 [9.3K]
2 years ago
11

Find the derivative of sin2X​

Mathematics
2 answers:
murzikaleks [220]2 years ago
7 0

Answer:

2cos2x

Step-by-step explanation:

Using the Chain rule

\frac{d}{dx} (sin2x)

= cos2x × \frac{d}{dx} (2x)

= cos2x × 2

= 2cos2x

inn [45]2 years ago
5 0

Step-by-step explanation:

Derivation using Product rule : -

To find the derivative of f(x) = sin 2x by the product rule, we have to express sin 2x as the product of two functions. Using the double angle formula of sin, sin 2x = 2 sin x cos x. Let us assume that u = 2 sin x and v = cos x. Then u' = 2 cos x and v' = -sin x. By product rule,

f '(x) = uv' + vu'

= (2 sin x) (- sin x) + (cos x) (2 cos x)

= 2 (cos2x - sin2x)

= 2 cos 2x

This is because, by the double angle formula of cos, cos 2x = cos2x - sin2x.

Thus, derivation of sin 2x has been found by using the product rule.

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