Misc 24 - Chapter 12 Class 11 Limits and Derivatives
Last updated at August 17, 2026 by Teachoo
Miscellaneous
Misc 1 (i)
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Transcript
Misc 24 Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): (ax2 + sin x)( p + q cos x) Let f (x) = (ax2 + sin x) (p + q cos x) Let u = ax2 + sin x & v = p + q cos x ā“ f(x) = uv So, fā(x) = (š¢š£)^ā² Using product rule = š¢^ā² š£+ć š£ć^ā² š¢ Finding uā & vā u = ax2 + sin x uā = (ax2 + sin x)ā = 2ax + cos x v = p + q cos x vā = (p + q cos x)ā = 0 + q (ā sin x) = ā q sin x Now, fā(x) = š¢^ā² š£+ć š£ć^ā² š¢ = (2ax + cos x) (p + q cos x) + ( ā q sin x) (ax2 + sin x) = ā q sin x (ax2 + sin x) + (p + q cos x) (2ax + cos x) (xn)ā = n xn ā 1 Derivative of sin x = cos x Derivative of cos x = ā sin x Derivative of constant = 0
