![Misc 24 - Chapter 13 Class 11 Limits and Derivatives - Part 2](https://d1avenlh0i1xmr.cloudfront.net/d1f9e3ab-260e-4c24-a526-0df03e06e742/slide73.jpg)
Miscellaneous
Last updated at April 16, 2024 by Teachoo
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