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Home » Find the derivative of the following functions (it is to be understood that and are fixed non-zero constants and and are integers):
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): \frac{{p{x^2} + qx + r}}{{ax + b}}
Class 11 | Limits and Derivatives | Maths | Miscellaneous Exercise | NCERT
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): \frac{{p{x^2} + qx + r}}{{ax + b}}

Suppose f(x) = \frac{{p{x^2} + qx + r}}{{ax + b}}

By applying quotient rule we get,

{f^\prime }(x) = \frac{{(ax + b)\frac{d}{{dx}}\left( {p{x^2} + qx + r} \right) - \left( {p{x^2} + qx + r} \right)\frac{d}{{dx}}(ax + b)}}{{{{(ax + b)}^2}}}

= \frac{{(ax + b)(2px + q) - \left( {p{x^2} + qx + r} \right)(a)}}{{{{(ax + b)}^2}}}

= \frac{{2ap{x^2} + aqx + 2bpx + bq - ap{x^2} - aqx - ar}}{{{{(ax + b)}^2}}}

= \frac{{ap{x^2} + 2bpx + bq - ar}}{{{{(ax + b)}^2}}}

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