C*X*U : Applying Product Rule To Find The Derivative

d/dx[cu]=

cu’

c * du/dx

In this expression, c represents a constant, and u represents a function of x. The derivative of cu with respect to x can be found using the product rule of differentiation, which states that the derivative of the product of two functions is equal to the first function multiplied by the derivative of the second function, plus the second function multiplied by the derivative of the first function.

So, applying the product rule to cu, we get:

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

Now, because c is a constant, its derivative with respect to x is equal to zero. Therefore, we can simplify this expression to:

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

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

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