Test:39 QNo:10

find dy/dx where y=tan^-1(2x/(1-x²))

2 Answers

Q10 find dy/dx where y=tan-1(2x/(1-x2))

a) 2/(1+x2)
b) 1/(1+x2)
c) 2/(1-x2)
d) 1/(1-x2)

Correct Answer: (a)

put x = tan \phi

\phi = \tan^{-1} x

y = 2\phi = 2tan^{-1}x

\frac{dy}{dx} =\frac{2}{1 + x^2 }

\frac{dy}{dx} = \frac{d \left(2 \tan^{-1} x \right)}{dx} = \frac{2}{1+ x^2 }

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