Find the derivative of the following function-fx-a x-b-p x2-q x-r

Here f(x)= ax+b/px^2+qx+r ∴ f'(x)= (px^2+qx+r) d/dx(ax+b) (ax+b)d/dx(px^2+qx+r)/(px^2+qx+r)^2 = (px^2+qx+r)(a) (ax+b)(2px+q)/(px^2+qx+r)^2 = apx^2+aqx+ar ...

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Standard XII

Mathematics

Parametric Differentiation

Find the deri...

Question

Find the derivative of the following function:
f(x)= $\frac{a x + b}{(p x^{2} + q x + r)}$

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Solution

Here $f (x) = \frac{a x + b}{p x^{2} + q x + r}$

$∴ f^{'} (x) = \frac{(p x^{2} + q x + r) \frac{d}{d x} (a x + b) - (a x + b) \frac{d}{d x} (p x^{2} + q x + r)}{(p x^{2} + q x + r)^{2}} = \frac{(p x^{2} + q x + r) (a) - (a x + b) (2 p x + q)}{(p x^{2} + q x + r)^{2}}$

$= \frac{a p x^{2} + a q x + a r - 2 a p x^{2} = a q x - 2 b p x - b q}{(p x^{2} + q x + r)^{2}}$

$= \frac{- a p x^{2} - 2 b p x + a r - b q}{(p x^{2} + q x + r)^{2}}$

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Find the derivative of the following function: f(x)= ax+b(px2+qx+r)

Here f(x)=ax+bpx2+qx+r ∴f′(x)=(px2+qx+r)ddx(ax+b)−(ax+b)ddx(px2+qx+r)(px2+qx+r)2=(px2+qx+r)(a)−(ax+b)(2px+q)(px2+qx+r)2 =apx2+aqx+ar−2apx2=aqx−2bpx−bq(px2+qx+r)2 =−apx2−2bpx+ar−bq(px2+qx+r)2

Find the derivative of the following function:
f(x)= $\frac{a x + b}{(p x^{2} + q x + r)}$