How To Differentiate U/V Using Quotient Rule Of Differentiation

d/dx[u/v]

(u’v-uv’)/v²

To solve this expression, we need to use the quotient rule of differentiation, which states that:

d/dx(u/v) = (v * d/dx(u) – u * d/dx(v)) / v^2

Using this formula, let’s differentiate the given expression:

d/dx(u/v) = (v * d/dx(u) – u * d/dx(v)) / v^2

Here, we can differentiate u and v separately, and then substitute their values in the above formula. Hence, we have:

Let’s start with du/dx:

d/dx(u) = du/dx = u’

Similarly, let’s find dv/dx:

d/dx(v) = dv/dx = v’

Now, substituting these values in the quotient rule formula, we have:

d/dx(u/v) = (v * u’ – u * v’) / v^2

Simplifying the above expression, we have:

d/dx(u/v) = (u’v – uv’) / v^2

Therefore, the derivative of u/v with respect to x is (u’v – uv’) / v^2.

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