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

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

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Byju's Answer

Standard XI

Mathematics

Derivative from First Principle

Find the deri...

Question

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

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Solution

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

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

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

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

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

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

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

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

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