How to Find the Derivative of the Quotient of Two Functions using the Quotient Rule

d/dx (u/v)

To find the derivative of the quotient of two functions u(x) and v(x), denoted as d/dx (u/v), we can use the quotient rule

To find the derivative of the quotient of two functions u(x) and v(x), denoted as d/dx (u/v), we can use the quotient rule. The quotient rule states that if we have two functions u(x) and v(x), then the derivative of their quotient is given by the following formula:

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

Here, du/dx represents the derivative of the numerator function u(x) with respect to x, and dv/dx represents the derivative of the denominator function v(x) with respect to x.

So, to find d/dx(u/v), you need to compute du/dx and dv/dx, and then use the formula above to find the derivative.

Let’s say we have functions u(x) = x^2 and v(x) = x. To find d/dx (u/v) in this case, we need to compute the derivatives of u(x) and v(x) first.

– du/dx = d/dx(x^2) = 2x
– dv/dx = d/dx(x) = 1

Now, substitute the values into the quotient rule formula:

d/dx (u/v) = (v * du/dx – u * dv/dx) / v^2
= (x * 2x – x^2 * 1) / x^2
= (2x^2 – x^2) / x^2
= x^2 / x^2
= 1

Therefore, d/dx (u/v) = 1 for the given functions u(x) = x^2 and v(x) = x.

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