Differentiate x2-5 x-6-4 x2-x-3

Using the quotient rule, we have d/dx ( x^2+5x 6/4x^2 x+3) =(4x^2 x+3).d/dx(x^2+5x 6) (x^2+5x 6).d/dx(4x^2 x+3)/(4x^2 x+3)^2 =(4x^2 x+3)(2x+5) (x^2+5x 6)(8x 1)/ ...

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Byju's Answer

Standard XI

Mathematics

Sigma n2

Differentiate...

Question

Differentiate $(\frac{x^{2} + 5 x - 6}{4 x^{2} - x + 3})$

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Solution

Using the quotient rule, we have

$\frac{d}{d x} (\frac{x^{2} + 5 x - 6}{4 x^{2} - x + 3})$

= $\frac{(4 x^{2} - x + 3) . \frac{d}{d x} (x^{2} + 5 x - 6) - (x^{2} + 5 x - 6) . \frac{d}{d x} (4 x^{2} - x + 3)}{(4 x^{2} - x + 3)^{2}}$

$= \frac{(4 x^{2} - x + 3) (2 x + 5) - (x^{2} + 5 x - 6) (8 x - 1)}{(4 x^{2} - x + 3)^{2}} = \frac{(9 + 54 x - 21 x^{2})}{(4 x^{2} - x + 3)^{2}}$

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Similar questions

Q. Differentiate

f (x) = 4 x^{2} - 5 x

Q. If

\frac{6 x^{2} - 5 x - 3}{x^{2} - 2 x + 6} \leq 4,

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(\frac{x - 3}{x^{2} - x - 6} + \frac{2 x - 1}{2 x^{2} + 5 x - 3} - \frac{2 x + 5}{x^{2} + 5 x + 6})

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Differentiate (x2+5x−64x2−x+3)

Using the quotient rule, we have ddx (x2+5x−64x2−x+3) =(4x2−x+3).ddx(x2+5x−6)−(x2+5x−6).ddx(4x2−x+3)(4x2−x+3)2 =(4x2−x+3)(2x+5)−(x2+5x−6)(8x−1)(4x2−x+3)2=(9+54x−21x2)(4x2−x+3)2

Differentiate $(\frac{x^{2} + 5 x - 6}{4 x^{2} - x + 3})$