Derivation of constant multiplied by a function ?

To derive a constant multiplied by a function, you can use the constant rule of differentiation.

Let's say we have a constant, c, and a function, f(x). The derivative of c times f(x) can be found as follows:

d/dx (c * f(x)) = c * d/dx (f(x))

In other words, the derivative of a constant times a function is equal to the constant multiplied by the derivative of the function.

For example, let's say we have the function f(x) = 3x^2. If we want to find the derivative of 5 times f(x), we can use the constant rule:

d/dx (5 * f(x)) = 5 * d/dx (f(x))

The derivative of f(x) = 3x^2 is f'(x) = 6x. Therefore, the derivative of 5 times f(x) is:

5 * f'(x) = 5 * 6x = 30x

So, the derivative of 5 times f(x) is 30x.