Ex 12.2, 11 (i) - Chapter 12 Class 11 Limits and Derivatives
Last updated at Dec. 16, 2024 by Teachoo
Ex 12.2
Ex 12.2, 1
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Transcript
Ex 12.2, 11 Find the derivative of the following functions: (i) sin x cos x Let f (x) = sin x cos x. Let u = sin x & v = cos x ∴ f(x) = uv So, f’(x) = (uv)’ = u’v + v’u Here, u = sin x So, u’ = cos x (𝐷𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒 𝑜𝑓 𝑠𝑖𝑛〖𝑥=𝑐𝑜𝑠𝑥 〗) & v = cos x So, v’ = – sin x Now, f’(x) = (uv)’ = u’v + v’ u = cos x . cos x + ( – sin x) sin x = cos2x – sin2x = cos 2x Hence f’(x) = cos 2x (𝐷𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒 𝑜𝑓 𝑐𝑜𝑠〖𝑥=〖− 𝑠𝑖𝑛〗𝑥 〗) (𝐷𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒 𝑜𝑓 𝑐𝑜𝑠〖𝑥=〖− 𝑠𝑖𝑛〗𝑥 〗)
