Find dy - dx if y- x-1 x-2 x-3

The correct option is A 3x^2+12x+11 Given, #160; #160; y= ( x+1 ) (x+2 #160; ) ( x+3 ) ⇒ y = x^3+6x^2+11x+6 ⇒dydx = 3x^2+12x+11 ...

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Algebra of Derivatives

Find dy / d...

Question

Find $\frac{d y}{d x}$ if $y = (x + 1) (x + 2) (x + 3)$

3 x^{2} + 12 x + 11

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x^{2} + 6 x + 11

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3 x^{3} + 11 x + 12

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3 x^{3} + 12 x + 6

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y = {sin}^{- 1} 2 x \sqrt{1 - x^{2}} + {sec}^{- 1} \frac{1}{\sqrt{(1 - x^{2})}},

\frac{d y}{d x} .

x = 0

\frac{x^{4} + 3 x^{3} - 3 x^{2} + 10}{{(x + 1)}^{2} (x - 3)}

y = {sin}^{- 1} (\frac{2 x}{1 + x^{2}}) + {sec}^{- 1} (\frac{1 + x^{2}}{1 - x^{2}})

\frac{d y}{d x}

y = {sin}^{- 1} \frac{2 x}{1 + x^{2}} + {sec}^{- 1} \frac{1 + x^{2}}{1 - x^{2}},

\frac{d y}{d x} = \frac{4}{1 + x^{2}} .

(1) {sin}^{- 1} (\frac{2 x}{1 + x^{2}}) = 2 {tan}^{- 1} x, | x | \leq 1

(2) {cos}^{- 1} (\frac{1 - x^{2}}{1 + x^{2}}) = 2 {tan}^{- 1} x, x \geq 0

(3) {tan}^{- 1} (\frac{2 x}{1 - x^{2}}) = 2 {tan}^{- 1} x, - 1 < x < 1

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