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# 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): (px² + qx + r)/(ax + b)

**Solution:**

The given function is f(x) =(px² + qx + r)/(ax + b). Using the quotient rule, its derivative is,

d/dx (f(x)) = [ (ax + b) d/dx (px^{2} + qx + r) - (px^{2} + qx + r) d/dx (ax + b) ] / (px^{2} + qx + r)^{2}

= [ (ax + b) (2px + q + 0) - (px^{2} + qx + r) (a + 0) ] / (px^{2} + qx + r)^{2}

= [ 2apx^{2} + aqx + 2bpx + bq - apx^{2} - aqx - ar ] / (px^{2} + qx + r)^{2}

= [apx^{2} + 2bpx + bq - ar] / (px^{2} + qx + r)^{2}

NCERT Solutions Class 11 Maths Chapter 13 Exercise ME Question 9

## 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): (px² + qx + r)/(ax + b)

**Summary:**

The derivative of the given function (px² + qx + r)/(ax + b) is [apx^{2} + 2bpx + bq - ar] / (px^{2} + qx + r)^{2}

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