How To Find The Derivative Of C Times U With Respect To X Using The Product Rule Of Differentiation

d/dx[cu]

cu’

To find the derivative of c times u with respect to x, we can use the product rule of differentiation.

Product rule states that if f(x) and g(x) are two functions of x, then the derivative of their product is given by:

(fg)’ = f’g + g’f

Here, c is a constant, and u is a function of x. So let’s use the product rule. We can write c as a constant factor of u, and u as a function of x, as follows:

f(x) = c and g(x) = u(x)

Using the product rule, we find that:

d/dx[cu] = d/dx[c]u + c d/dx[u]

Since c is a constant, its derivative d/dx[c] is 0. So the derivative of cu with respect to x simplifies to:

d/dx[cu] = 0 + c d/dx[u]

This means that the derivative of c times u with respect to x is equal to c times the derivative of u with respect to x.

Therefore, we can write the final answer as:

d/dx[cu] = c d/dx[u]

More Answers: