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Find the slope of the curve y = Inx at x=2​

Answer 1

Question:-

Find the slope of the curve y = lnx at x = 2 .

Answer:-

1/2

Solution:-

We know that the first derivative of the equation of any curve at a point gives the slope of the tangent of the curve at that particular point.

Here,

The given curve is ,

y = lnx

Now,

Differentiating both sides of the given equation with respect to x , we get;

=> dy/dx = d(lnx)/dx

=> dy/dx = 1/x

=> (dy/dx) at x = 2 will be 1/x = 1/2 .

Hence,

The required slope is 1/2 .