Question

Find dy/dx,when x=log(xy)

Answer 1

Answer :

We know that, log (xy) = logx + logy

Given that,

    x = log (xy)

    ⇒ x = logx + logy .....(i)

Now, differentiating both sides of (i) with respect to x, we get

    d/dx (x) = d/dx (logx) + d/dx (logy)

    ⇒ 1 = 1/x + (1/y) (dy/dx)

    ⇒ (1/y) (dy/dx) = 1 - 1/x

    ⇒ (1/y) (dy/dx) = (x - 1)/x

    ⇒ dy/dx = {(x - 1)y}/x

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