Question

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): \(\frac{px^2+qx+r}{ax+b}\)

Answer 1

=\(\frac{-apx-2bpx+ar-bq}{(px^2+qx+r)^2}\)
Let f (x)= \(\frac{px^2+qx+r}{ax+b}\)
By quotient rule,
f'(x)= (ax+b)\(\frac{d}{dx}\)(px²+qx+r)- (px² +qx+r)\(\frac{d}{dx}\)\(\frac{(ax+b)}{(ax+b)^2}\)
=(ax+b)(2px + q) -(px²+qx+r)\(\frac{(a)}{(ax+b)^2}\)
=\(\frac{-apx^2+2bpx+bq-ar}{(ax+b)^2}\)