How to Find the Derivative of the Product | Derivative of k*f(x) with Respect to x

d/dx k*f(x)

The expression d/dx is called a derivative operator, which represents the derivative with respect to the variable x

The expression d/dx is called a derivative operator, which represents the derivative with respect to the variable x. In this case, we are taking the derivative of the function k*f(x) with respect to x.

To find the derivative, we can use the product rule of differentiation. The product rule states that if we have two functions u(x) and v(x), the derivative of their product is given by:

d/dx (u(x) * v(x)) = u(x) * v'(x) + v(x) * u'(x)

In our case, u(x) = k and v(x) = f(x). Let’s find the derivatives of these functions first:

du/dx = 0 (since k is a constant, its derivative is 0)
dv/dx = f'(x) (the derivative of f(x) with respect to x, denoted as f'(x))

Now we can apply the product rule:

d/dx (k * f(x)) = k * f'(x) + f(x) * 0
= k * f'(x) + 0
= k * f'(x)

So, the derivative of k*f(x) with respect to x is k times the derivative of f(x) with respect to x, which can be written as k * f'(x).

In simpler terms, the derivative of k*f(x) is equal to k times the derivative of f(x).

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