Using the chain rule... how can i differentiate this?
y=x�ã(x-2)
I do not know what a with an umlaut over it means.
If I recall, this means √ (the dager of copy/paste from word processor screens)
If that is so, then
y = x√(x-1)
using the product rule, if
y = uv
y' = u'v + uv'
y' = (3x-2)/(2√(x-1))
To differentiate the function y = x^2(x-2), we can use the chain rule. The chain rule states that if we have a composite function y = f(g(x)), then the derivative of y with respect to x is given by dy/dx = f'(g(x)) * g'(x).
Let's break down the function y = x^2(x-2) into two parts: f(u) = u^2 and g(x) = x - 2.
First, let's find the derivative of f(u) = u^2. This is a simple power rule differentiation: f'(u) = 2u.
Next, let's find the derivative of g(x) = x - 2. This is also a simple differentiation: g'(x) = 1.
Now, we can apply the chain rule: dy/dx = f'(g(x)) * g'(x).
Substituting f'(u) = 2u and g'(x) = 1, we get dy/dx = 2(x - 2) * 1.
Simplifying the expression, we have dy/dx = 2(x - 2).
Therefore, the derivative of y = x^2(x-2) is dy/dx = 2(x - 2).