\frac{d}{dx}\left [ log(e ^{x}(\frac{x-2}{x+2}^{3/4})\right ] is equal to

  • Option 1)

    1

  • Option 2)

    \frac{x^{2}+1}{x^{2}-4}

  • Option 3)

    \frac{x^{2}-1}{x^{2}-4}

  • Option 4)

    e^{x}.\frac{x^{2}-1}{x^{2}-4}

 

Answers (1)

As we learnt in 

Differential Equations -

An equation involving independent variable (x), dependent variable (y) and derivative of dependent variable with respect to independent variable 
\left (\frac{\mathrm{d} y}{\mathrm{d} x} \right )

- wherein

eg:

  \frac{d^{2}y}{dx^{2}}- 3\frac{dy}{dx}+5x=0

 

 = \frac{d}{dx}(loge^{x}(\frac{x-2}{x+2})^{\frac{3}{4}})

= \frac{d}{dx}(loge^{x}+\frac{3}{4}(log\frac{x-2}{x+2}))

= \frac{d}{dx}(x+\frac{3}{4}[log(x-2)-log(x+2)])

= 1+\frac{3}{4}[\frac{1}{x-2}-\frac{1}{x+2}]

= 1+\frac{3}{4}[\frac{4}{x^{2}-4}]

= 1+\frac{3}{x^{2}-4}\:\:\:=\frac{x^{2}-1}{x^{2}-4}

\frac{y-1}{x-1}= e^c = K

\frac{x-1}{y-1}=c


Option 1)

1

Incorrect

Option 2)

\frac{x^{2}+1}{x^{2}-4}

Incorrect

Option 3)

\frac{x^{2}-1}{x^{2}-4}

Correct

Option 4)

e^{x}.\frac{x^{2}-1}{x^{2}-4}

Incorrect

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