what is derivative of (1-2x)^-1?
is it -1/(1-2x)^2 ?
To find the derivative of the function (1 - 2x)^-1, you can use the chain rule. The chain rule states that if you have a composite function f(g(x)), then the derivative of f(g(x)) with respect to x is equal to the derivative of f with respect to g, multiplied by the derivative of g with respect to x.
Let's start by rewriting the given function as (1 - 2x)^(-1) = 1 / (1 - 2x).
To differentiate 1 / (1 - 2x), you need to differentiate both the numerator and the denominator separately and apply the quotient rule.
The numerator is a constant, so its derivative is zero.
To find the derivative of the denominator, you can use the power rule. The derivative of (1 - 2x) is equal to -2.
So, applying the quotient rule, the derivative of the function is:
[0 * (1 - 2x) - 1 * (-2)] / (1 - 2x)^2
This simplifies to:
2 / (1 - 2x)^2
Therefore, the derivative of (1 - 2x)^-1 is 2 / (1 - 2x)^2.