Differentiate.
y = (cx)/(1 + cx)
g(x) = 1 + cx
f(x) = cx
Using the quotient rule:
y' = [(1 + cx)(f') - (cx)(g')]/(1 + cx)^2
How do you find f' and g' when there is more than one variable? Having a C and an X?
was it also said that you would treat c as another variable? because in most problems, c is treated as a constant.
thus:
f'(x) = c
g'(x) = c
When differentiating functions with multiple variables, such as in the case of f(x) = cx and g(x) = 1 + cx, we need to apply the partial derivative with respect to the variable we are differentiating.
To find f'(x), we need to take the partial derivative of f(x) = cx with respect to x. Since f(x) contains only one variable, x, the partial derivative is the same as the ordinary derivative. Thus, f'(x) = c.
To find g'(x), we also take the partial derivative of g(x) = 1 + cx with respect to x. In this case, we differentiate each term separately. The derivative of 1 with respect to x is 0 because the constant term does not change with x. The derivative of cx with respect to x is simply c, as the variable x is being differentiated with respect to itself. Therefore, g'(x) = c.
By finding f'(x) = c and g'(x) = c, you can substitute these values into the quotient rule to differentiate y = (cx)/(1 + cx).