Question

How To find the derivative of a function?? If the question given is 2/x​

Answer 1

Answer:

let function is f (x) = 2/x

now differentiation with respect to x

d/dxf(x)=d/dx2/xd/dxf(x)=d/dx2/x

d/dxf(x)=2d/dx(x)−1d/dxf(x)=2d/dx(x)−1

d/dxf(x)=−2(x)−2d/dxf(x)=−2(x)−2

d/dxf(x)=−2/x2

This is the same as ddx(2∗x−1)ddx(2∗x−1)

The two can be pulled out to get 2∗ddx(x−1)2∗ddx(x−1)

And the derivative of any x^a is ax^{a-1}, or in this case 2∗(−x−2)2∗(−x−2)

Calculating this yields −2x−2

Here y= 2/x

Differentiating both sides with respect to x

dy/dx = 2d(1/x)/dx

dy/dx = 2dx^-1/dx

dy/dx = 2. -1.x^-1-1

dy/dx = -2x^-2

dy/dx = -2/x^2

ddx(2x)ddx(2x)

=2⋅ddx(1x)=2⋅ddx(1x)

=2⋅−1x2=2⋅−1x2

=−2x2