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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