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Last updated at May 29, 2023 by Teachoo

Example 21 Compute derivative of (i) f(x) = sin 2x Let f (x) = sin 2x = 2 sin x cos x Let u = 2 sin x & v = cos x So, f(x) = uv ∴ f’(x) = (uv)’ = u’v + v’u Here, u = 2 sin x u’ = 2 cos x & v = cos x v’ = – sin x f’(x) = (uv)’ = u’v + v’ u = 2 cos x . cos x + 2 sin x ( – sin x) = 2 cos2 x – 2 sin2 x = 2 (cos2 x – sin2 x) ∴ f’(x) = 2 (cos2 x – sin2 x) (𝐷𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒 𝑜𝑓 𝑠𝑖𝑛〖𝑥=𝑐𝑜𝑠𝑥 〗) (𝐷𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒 𝑜𝑓 𝑐𝑜𝑠〖𝑥=〖− 𝑠𝑖𝑛〗𝑥 〗)