The Product Rule of Differentiation: Finding the Derivative of the Product of Two Functions

d/dx [uv]

To find the derivative of the product of two functions defined as u(x) and v(x) with respect to x, we use the product rule of differentiation

To find the derivative of the product of two functions defined as u(x) and v(x) with respect to x, we use the product rule of differentiation.

The product rule states that the derivative of the product of two functions is given by:

d/dx [u(x) * v(x)] = u(x) * dv/dx + v(x) * du/dx

This means that we take the derivative of the first function, u(x), and multiply it by the second function, v(x). Then we add to this the product of the first function, u(x), and the derivative of the second function, dv/dx.

So, applying the product rule to d/dx [uv], we have:

d/dx [uv] = u(x) * dv/dx + v(x) * du/dx

Since u and v are just variables, we can rewrite this as:

d/dx [uv] = v * du/dx + u * dv/dx

Therefore, the derivative of the product uv with respect to x is v times the derivative of u with respect to x plus u times the derivative of v with respect to x.

More Answers: