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):
\( \dfrac{ax+b}{px^2+qx+r}\)
Let f(x) \( \dfrac{ax+b}{px^2+qx+r}\)
By quotient rule,
\( \dfrac{(px^2+qx+r)(a)-(ax+b)(2px+q)}{(px^2+qx+r)^2}\)
\( \dfrac{(apx^2+aqx+ar-aqx+2npx+bq)}{(px^2+qx+r)^2}\)
\( \dfrac{-apx^2+2bpx+ar-bq}{(px^2+qx+r)^2}\)
Differentiate with respect to x xn loga x
Differentiate with respect to x xn tan x
Differentiate with respect to x x2 ex log x
Differentiate with respect to x x3 ex
Differentiate with respect to x x3 sin x
